3- square root (2m + 2) = 8 Even Good Math Students will make this ERROR!

[@floridian2023]

Thanks!

[@charlesmitchell5841]

Considering how many kids are flunking math, your channel should be the most popular one on KZbin! If it’s not, then that is a shame.

[@Fauxgypsies2023]

Where will any of this be applicable in the real world by the vast majority of humans? Former Math major from many moons ago. 😊

[@tomtke7351]

Even more SIGNIFICANT is that if a viewer is missing understanding a presentation that John offers that viewer can EASILY rewind and repeat as much as necessary......

[@Fauxgypsies2023]

@@tomtke7351 oh, I solved this basic algebra. But I am responding to the notion something is amiss with students in 'flunking' math! No, the school system is flunking in providing real education. And....tommy...you could just as easily not respond with a meaningless comment. 😊

[@MrSummitville]

​@@Fauxgypsies2023 Engineers use this. Workers at McDonald's do not.

[@Fauxgypsies2023]

@@MrSummitville they do? What is the application?

[@floridian2023]

Thanks for your lessons!

[@Kleermaker1000]

Null. :)

[@tomtke7351]

New algebra students... algebra typically involves an equation with elements left/right separated by the equal (=) sign. Keep both sides equal. Manipulation/resolution is achieved by acting equally to BOTH SIDES. New algebra students commit this to memory: treat both sides of equation with equal methods.

[@OscarMorales-wn7ql]

Good morning! For a student who has been working on the concept of raising the number in the field of real numbers, the equivalent equation is V(2m+2) = -5 It has no solution in the field of real numbers, because: 0< V(2m+2) =-5 < 0 is a contradiction. Good day!

[@gavindeane3670]

It has no solution in real numbers or complex numbers.

[@herbertklumpp2969]

Per Def. Is sqrt (a) >=0 therefore 3 - sqrt

[@MaydayAggro]

Took me literally 2 seconds to answer this question. Substitute x for 2m + 2, just to make it easier to deal with; 3 - sqrt x = 8; sqrt x = -5; null because principal sqrt cannot be negative.

[@debbieholoquist2059]

Lesson learned: don't be so confident that you fail to check for extraneous solutions.

[@badblock8259]

Instead of null, would an imaginary number work? For instance, would 23/2i squared work?

[@marknieuweboer8099]

No, the square root of an imaginary number can't be negative either (I had to look it up). To solve this we'd need a new set of numbers with sqrt(j) defined as -1. I have no idea if someone has ever tried this. Then we'd get sqrt(2m + 2) = 5.sqrt(j) => 2m + 2 = 25.j => m = 12½j - 1

[@jpdemer5]

The answer is "null" if you adhere to a convention of algebraic notation. It's the same convention that calls for plotting y=sqrt(x) as only the top half of a parabola, omitting the half that lies below the x axis. This is done because algebra requires y to be a "function" of x; it's part of the _definition_ of a function that there's a one-to-one correspondence between values of x and values of y. That's how it works in algebra. In other applications, such as analytic geometry, you don't ignore the negative roots.

[@gavindeane3670]

Nobody is ignoring negative roots. This expression just happens to refer only to the principal square root. That's what the √ symbol means.

[@donutschool]

Its worth remembering that while mathematics might be based on beautiful, absolute fundamental truths about the universe, truths that can be proven beyond all doubt using only logic, mathematical *notation* is an arbitrary and changeable set of rules made up by fallible humans which, like any human language, is only really defined by current usage - and this problem is very much about *notation* rather than mathematical truths. The radical "tick" symbol is widely agreed to mean the positive square root (or principal root if you're getting into complex numbers) - I think so, Wikipedia thinks so... and even that "the square root" means the principal root, but there seems to be a distinct lack of *primary* sources online (who knows how convention has changed since Pythagoras, and Newton didn't even get the notation for calculus right! :-) ). My ancient dead-tree copy of the "Penguin Dictionary of Science" states that √9=+/-3 but, frankly, I have no problem distrusting that as a source. The strongest arguments seem to be that it makes sense as a convenient notation because (a) it's usually what you want and (b) it makes radicals single-valued and therefore valid functions. Plus, why else would you need a "+/-" in the famous quadratic formula? Of course, almost every calculator, programming language or set of tables gives *positive* square roots - if the person who wrote the expression intended the negative root to be considered they should have stuck a "+/-" in front of it! However, I distinctly remember being taught in school that the answer to "What is the square root of (say) 100" is "+10 or -10" (lose a mark if you forget the negative one) which - with hindsight - doesn't even make *grammatical* sense. Whether that was ever presented using the radical symbol I can't remember, but the fact that the symbol was *defined* as the positive/principal root was something I had to look up later in life (and, frankly, *that* is a lottery) so I have a lot of sympathy for people who just didn't know... See also all of the "many will get this wrong" problems about order-of-operations (usually contrived by mixing the division operator that nobody uses with implied multiplication) which are also all about arbitrary notation conventions rather than mathematical truths.

[@TomJones-tx7pb]

Good comment. Personally, I am a seeker of truth and insight, and you have to be careful about this issue when using Mathematica. The definition of "square root" that I go by is "a number which, when squared..." The reason being, that it is the definition that usually maps onto the situation at hand. There are two parabolas that land a thrown ball at the same spot, and to find one of them you have to use the negative value of a square root.

[@gavindeane3670]

100 has two square roots, √100 which is 10 and -√100 which is -10. "What is the square root of 100?" is not the same question as "What is √100?" The answer to the first question is "100 has two square roots. They are 10 and -10." The answer to the second question is 10.

[@donutschool]

@@gavindeane3670 ...your answer is perfectly correct, but when a question explicitly asks for *the* square root then just giving the principal square root should be perfectly reasonable. Almost everywhere "square root" (singular) is used, it refers to the principal square root. Even my old mathematical tables just have a table titled "square roots" - not "positive square roots" and no minus signs in sight. If you ask someone for the cube root of 27 would you expect all *three* answers (one real, two complex)? If someone reads "What is √100?" out aloud - what words come out of their mouth? Do they really always say "What is the *principal* square root of √100"? This isn't about right/wrong - but If you want both roots ask for the square *roots* or the solutions to "x^2=100". Asking a sloppy question and expecting a rigorous answer to the real question in your head could end up with people thinking that √100 = +/-10 (or just hating math).

[@gavindeane3670]

The obvious source to look at for an authoritative definition is ISO 80000-2, which defines √x as positive for positive x (i.e. √x is the principal square root of x).

[@TomJones-tx7pb]

@@gavindeane3670 Nice find. And what does it define it to be for not positive x? Does this video say 2m+2 is positive? I regard this whole video as mathematical trolling for non-mathematicians..

[@davesreb]

I don’t understand why this was so complicated. Subtract 3 from both sides and you have a negative number (-sqrt(2m+2)) = 5. When you write sqrt(###) it is always assumed to be positive. If you mean the negative sqrt, you need to indicate that with a negative sign: -sqrt(2m+2). If it could be either, you need to use +/-.

[@TomJones-tx7pb]

Actually, no. When I am modeling a physical situation with an equation, I allow the square root to be a complex number. Otherwise you cannot solve a lot of problems in fluid dynamics.

[@davesreb]

@@TomJones-tx7pb Tom, that’s different. If, for example, m=-1, -sqrt(2m-2)=-sqrt(4)=-2i only (not +/- 2i, and not +2i).

[@TomJones-tx7pb]

@@davesreb To put what I am saying another way, a function is not well defined unless you specify the range and domain of the function. Leaving that ambiguous creates KZbin videos like this one with people debating undefined semantics. If you want to use math to describe physical models, you need the boundary conditions and spaces you are working with to be large enough to contain the problem you are working with, but ideally not too large that they allow false solutions. Working with only positive real numbers is totally inadequate for many problems because it is not a field that gives all roots of polynomials. Modern scientists usually work with equations over the complex field for this reason, whether they realize it or not, and the equations have this as an implicit assumption.

[@davesreb]

@@TomJones-tx7pb The solution to this problem is a number m such that sqrt(2m-2) is equal to negative 5. And in the set of real or complex numbers, there is no such number m. There is a solution to 3+sqrt(2m-2)=8 (m=27/2), but there is no solution to 3-sqrt(2m-2)=8.

[@TomJones-tx7pb]

@@davesreb Any complex number has 2 square roots in the complex field. f(x) = 2x - 2 is an invertible function. Put the two together, and what have you got? Implicitly assuming that you only look at the solutions of a function that are positive real numbers is useful for looking up approximate values in tables, and you can usually derive the other possible values of the function from them. What a scientist loosely calls an equation is often different to the precise definition of a similar function in mathematics, BTW. An example would be x*x + y*y = 1. y is not a function of x, but the set of points that satisfy the equation with x and y being real numbers form a unit circle in the real RxR plane. I have never heard anyone argue that only one quadrant of the circle is valid.

[@Roboticgladiator]

null. Squaring both sides to flip the sign is mathematical shenanigans.

[@josephlaura7387]

a) 23/2

[@b213videoz]

square_root(2m+2) = - 5 ...well, there is no way a square root of (2m+2) can be a negative number so the answer is d) null

[@richardcommins4926]

Let X = sqrt(2*m + 2) and rewrite the formula to 3 - X = 8 . The only answer to this problem is that X has to equal - 5. The square root of a positive number is always positive so the wrong answer because m = 23/2 can never give a negative answer so that answer is wrong and the correct answer is null. Yes, I know the sqrt(25) can be solved by 5 * 5 and - 5 * - 5. When you are dealing with a polynomial that has 2 answers the use of the +/- to get the two answers to that type of problem is OK. In this case you can't use both answers to solve the problem because there can only be one solution and both solutions won't work. That is why the principal square root was defined as only positive numbers so you don't have to pick an answer. The only time a square root can produce a negative answer is when you are using imaginary numbers where i^2 = -1 or i = sqrt (-1) and was not included in this problem. Then the sqrt(-25) can be rewritten to be sqrt (25) * sqrt(-1) = 5 * i . Another was to look at it is when dealing with functions e.g. in calculus, a function must map an x to a single y. So we are only interested in the principal root. All the principle square root is a convention (or rule) to prevent confusion.

[@MaydayAggro]

I worked this similarly. Let x = 2m + 2.

[@gavindeane3670]

It wouldn't matter if imaginary and complex numbers were included in the question. There's still no value of z to satisfy √z = -5.

[@InPursuitOfCuriosity]

Why can't you move the radical onto the other side of the equation, thus removing the issue of a negative square root? If you do this you will eventually get -5 = sqrt of 2m+2, which if you square both sides will give you 25 = 2m +2 ---> 23/2. Edit: Oh i see, you would need to make it "sqrt of -2m - 2" which would also cause issues.

[@gavindeane3670]

No, you wouldn't need to make it √(-2m - 2). Moving the radical to the other side to get -5 = √(2m + 2) is fine. But now you have an impossible equation because -5 cannot equal √(anything).

[@josephlaura7387]

Thank you ☺️

[@MrSeezero]

Actually, if you look at the equation and consider how principal roots work, you don't even have to attempt to solve for m to get the answer. If the value coming out of the radical has to be equal to negative 5 in order for the expression on the left to be equal to 8, then you should immediately pick "null" as the answer since the other square root coming from the radical would have to be positive 5 which would be the principal root of that radical and be the one that you would be forced to use. Thus, there would be no solution. Now if this weren't a multiple-choice question, then you might still have to go through the motions of solving for m and then show that the value that you got for m would not work to show that the answer would be null.

[@gavindeane3670]

Even without the multiple choice options, as soon as you realise you have √(something) = -5 you know that there is no solution.

[@tobymichaels8171]

Please explain how the contemporary concept of "principle square root" is anything but arbitrary

[@MaydayAggro]

It's nothing but arbitrary, and I hate it.

[@gavindeane3670]

Well it makes the √ symbol useable, so there's that.

[@MrSummitville]

@toby - What do you mean by "contemporary concept" ? The square root of a positive number has been a positive result since the 1st Century!

[@tobymichaels8171]

@@MrSummitville What I mean is that since probably the Islamic Golden Age at the very least the late Renaissance it has been common knowledge that a positive number has both a positive and negative square root. The concept that the positive root is somehow more real and has primacy over the negative root is what seems to me a contemporary affectation. Nothing of the sort was taught in either high school or college as late as 1995, by my experience at least. I would have to see some logical proof to accept this notion as anything but arbitrary.

[@thomasharding1838]

According to standards, the square root of an unknown is positive and negative unless specified. Since 'm' in this problem is unknown, "2m+2" is unknown and therefore the square root would be positive and negative. Therefore, subtracting 3 from both sides results in 0 minus the positive or negative square root of (2m+2) = 5. Squaring both sides give 0 minus positive or negative (2m +2) = 25. 0 minus negative (2m + 2) = 25 results in 0 + 2m + 2 = 25 and therefore 2m = 23 and m = 23/2. If m is unknown, then "2m +2" is unknown.

[@gavindeane3670]

I'm not sure where you got that from. There is nothing different about how we treat unknown values and known values. The point here is that it IS specified that we are referring only to the principal square root. That is what the √ symbol means. And since -5 cannot be the principal square root of anything, the equation is simply invalid.

[@thomasharding1838]

@@gavindeane3670 There are several significant Universities' websites that are very specific about this.

[@gavindeane3670]

@@thomasharding1838 Are you sure you're not misunderstanding their point? It is certainly true that when we're dealing with an unknown value x and we have an equation in x² then we need to consider both square roots. But that is completely different to suggesting that the radical symbol changes its meaning depending on whether its operand happens to include an unknown. The guy who runs this KZbin channel makes that mistake but I'd be surprised if any university mathematics department did. Have you got any examples?

[@thomasharding1838]

@@gavindeane3670 I didn't want to name names but Harvard and Cornell. If it is the root of an unknown the default answer is the plus and minus roots unless either one is specified. But if it is the root of a positive number, the default is the principal (positive) root unless plus and/or minus is specified.

[@gavindeane3670]

​@@thomasharding1838You really need to consider the possibility that you have misunderstood their point. The giveaway is your use of the phrase "unless either one is specified". When you see the √ symbol it is, by definition, ALWAYS specified which square root(s) the author is referring to. If they write √x they are referring to the principal square root. If they write -√x they are referring to the other square root. And if they write ±√x they are referring to both square roots. If YOU are the author, the responsibility is on you to understand which square root(s) are relevant in your particular circumstance and to write accordingly. Almost certainly, this will be the actual point of whatever it is you've read from these universities: reminding you that when dealing with unknowns, it is generally the case that you need to consider both square roots (so by implication, you should generally be writing ±√x not √x). Those are some prestigious universities you've mentioned. Think about it for a moment. Do you really believe that mathematicians at that level would tell you that the answers to the questions "What is the value of √49?" and "What is the value of √x for x=49?" are different? I don't. Do you really believe that mathematicians at that level would accept such a woolly and vague definition of the √ symbol as "either or both of the square roots, whichever you happen to find convenient", which is how you're interpreting it here? I don't. Do you really believe that mathematicians at that level would take a mathematical symbol that already gives us a clear and precise way to refer to just one of the square roots, a clear and precise way to refer to just the other square root, and a clear and precise way to refer to both square roots, and dispense with all that and invent their own meaning instead? I don't. There's not just the utterly baffling question of WHY you'd think they would do that. There's also the how. How would it even work? How is the author supposed to indicate which specific square root they are referring to (or both), if the √x and -√x and ±√x meaning doesn't apply? What do you think they do instead?

[@russelllomando8460]

Got it null. None of the supplied answers complete the equation. Thanks for the fun.

[@MargaretCutt-um8iq]

Ugh show it right first...showing it wrong reinforced error......

[@charlesmitchell5841]

A) 23/2 ?

[@HighKingTurgon]

isqrt5/2 - 1

[@gavindeane3670]

Did you actually try that? If that is the value of m then 2m + 2 is i√5. So we would have 3 - √(i√5) which doesn’t equal anything like 8.

[@HighKingTurgon]

@@gavindeane3670 I genuinely have no memory of watching this video. I wonder if my reply was from an autoplay to another video?

[@dennismasel206]

Null

[@cindycain3301]

First thing you do is subtract 3 from both sides

[@mawavoy]

D

[@StarSong936]

Well, I came up with if it's not 23/2 then it's null. So, I guess I'll give myself .5 points.

[@terry_willis]

What math genius created the concept that the "principal sq rt" can only be positive? It appears this idea was devised to make mathematics seem more difficult and confuse students. Other than just declaring it's a math maxim, what is the rationale?

[@MrSummitville]

If you want both the plus and the minus root then you must explicitly indicate +/-sqrt(25). It is just one of the laws of math. If you want an example of explicit +/- roots then review the formula to find the roots of a quadratic equation.

[@jpdemer5]

@@MrSummitville It's a convention, not a "law".

[@MrSummitville]

@@jpdemer5 Unless otherwise stated, the square root of a positive number, *always* returns positive answer. The word *always* makes it one of the many mathematical laws. No, you do not have a choice.

[@jpdemer5]

@@MrSummitville And who put the "always" in there? Nature? Or the people who wrote the rules?

[@gavindeane3670]

The rationale is to give the √ symbol a clear meaning and make it easy to use precisely. Precision is obviously important in mathematical notation. The principal square root of x is √x, the other square root is -√x, and if you want both square roots (eg the quadratic equation formula) you can write ±√x. What's the alternative?

[@sinalde4728]

Please make it easy: simply stop, when you see, that root = -5! No real solution exist , then!

[@gavindeane3670]

No solution exists at all, real or complex.

[@c_b5060]

I enjoy learning about this topic, buy please don't treat me like a moron. You do not, not, not need to circle each answer as you mention it.

[@sirbrad2336]

He's a great teacher. Lighten up.

[@kuriachankk6751]

A

[@stompthedragon4010]

I'm starting to hate math even more. This sounds like loop,- di-loop loop- di-li to me.

[@happybee0622]

23/2

[@AnneNissen-nk4mh]

You are good too teach others but one problem you have is you talk to much.

[@MrSummitville]

It is a math class.

[@cindycain3301]

Top much yakity yak yak. No Wonder the kids are confused. Just show how to recognize and solved the problem! No yakity yak yak!

[@cindycain3301]

Gosh, can't watch anymore .. what a waist of time and breath!

[@playgirl7305]

Fcuk the princepal square root. Who defined it to be that anyway.

[@gavindeane3670]

Probably somebody who wanted the √ symbol to be useable.

[@MrSummitville]

@PlayGirl - The Greek mathematians in the 1st Century.

[@chrisweber2552]

You talk too much.

[@MrSummitville]

It's a math class.

[@cindycain3301]

Yakity yak yak! Unbelievable! Bad teaching!

[@Facefur1]

I find that declaring that the only valid answer for root(25) is positive to be, at best, confusing. If +- is valid for a quadratic, it's valid for this. First time I disagreed with your answer and your rationale. Plug in 23/2, use the negative value, and you get a correct answer, so I claim you're incorrect at null.

[@MrSummitville]

There is no such thing as ... "use the negative". sqrt(25) is equal to 5.

[@donutschool]

Replace the square root sign with “(2m + 2)^(1/2”) and you’d be right. You’re not really getting the maths wrong, it’s just that there’s an arbitrary convention that you didn’t know about (forgivable, since it is often badly taught in school). The radical “tick” symbol is *defined* as the principle root (positive, for the square root) It’s not some deep, fundamental truth of the universe - someone has just sat down and decided that makes the most sense as a convenient notation (which becomes more obvious when you get on to higher roots and complex numbers). It also makes the radical symbol a true “function” with only one output for each input. That’s why, for example, the famous formula for solving quadratics has an explicit “+/-“ sign in it (why would you need that if it was built in to the square root sign?). . Remember, problems like this are deliberately contrived to trip up people who don’t know these technical wrinkles. If you introduce a root symbol, it’s up to you to decide whether a +/- is needed (if it’s, say, the length of a side of a triangle, probably no - if you just square rooted both sides of the equation, probably yes). See also all of the trick “PEMDAS” problems that throw you off by using the “division” sign in ways that most mathematicians would avoid. School really sets people up for this by gleefully using the negative root as a gotcha when solving simple quadratics but never mentioning why this doesn’t apply to problems with the radical sign. I’ve even seen a textbook that, in its introduction to functions, used the square root as its prime example of “not a function” because it wasn’t single valued. That falls under “not technically wrong but a great way to confuse people” I think…

[@Facefur1]

@@MrSummitvilleWell, (-5)^2 = 25, and (5)^2 = 25, so i disagree. Whatever convention he asserts was not taught when i was in school 9through masters level courses.

[@MrSummitville]

@@Facefur1 There is no "SQUARE( )" function in the example formula. Therefore, you are still wrong.

[@Facefur1]

What does that have to do with anything? the author has already acknowledge that his answer is based on "convention", which is a nice way of saying "We picked an arbitrary way to do this.".

[@pennstatefan]

The answer is 23/2.

[@TomJones-tx7pb]

wow math is used to solve problems, many of which lie in the complex plane, not restricted to real numbers. As a mathematician and scientist I would be ashamed to post this dogmatic video which misleads. Last time I looked a quadratic has 2 solutions that vary by whether you take the positive value of a square root or the negative value.

[@gavindeane3670]

The formula for solving a quadratic equation has the ± symbol in front of the √. That's because it needs BOTH square roots of the (b² - 4ac) term. The question in this video does not refer to ±√(2m+2) so we know we're not dealing with both square roots here.

[@MrSummitville]

@TomJones - Except this is *NOT* a Quadratic Equation. Where do you see "m" squared?

[@TomJones-tx7pb]

@@MrSummitville I agree about that.

[@jald910]

Null

[@sekharb6651]

23/2