The square root of 8 x the square root of 2 divided by square root of 8 x square root of 2 = 1?

[@nancyholcombe8030]

No. The answer is 2. Your explanation is great!😊

[@paulconway2963]

it's the age old problem of BODMAS and PEMDAS or whichever other you prefer, being applied mindlessly without understanding what it means... As a primary school pupil.. the first version of the mnemonic I was taught was Bless My Dear Aunt Sally - except the teacher went to great pains to write it as Bless My Dear Aunt Sally and at the same time stressing that if they are on the same line, then they are treated equally and you deal with them left to right as you come across them. (and as such you can reorder the "operation+operand" pairs to make the arithmetic easier - we all do it easily enough when it comes to revenue and expenditure (count all the cash you get in first, then see how much is left after you pay the bills) - people seem to have a real blindspot in their understanding applying the add/subtract processing to multiply/divide puzzles

[@thenetsurferboy]

Yes it is a puzzle wondering what the author implied But left to right does not enter in any mathematical expression Just follow the rules

[@RobertMartin-j9f]

super simple using PEMA which relies on two rules: 1:) when dividing by a fraction you take the reciprocal and make it multiplication 2:) x - y is the same as -y + x and -x - y is the same as -y + -x Apply that here we "see" the divided by number as x over 1 which makes it a fraction so we turn it into multiplication by making it 1 over x. This means the two square roots of 8 cancel out to just 1. 1 * 2^1/2 * 2^1/2 becomes (1 * 2 * 2)^1/2 which is 4^1/2 or just 2. (remember when we have a fraction as an exponent the numerator is a power and the denominator is the root)

[@ExileXCross]

Just turn all the operations into multiplication √8 • √2 • (1/√8) • √2 = 2

[@Dr_piFrog]

Why does PEMDAS start with the letter "P" for Parentheses -- perhaps this is important to notice. Concepts of mathematics that are overlooked here are those of preciseness and precision. Blindly writing mathematical expressions using PEMDAS tends to put these quantities on the back-burner so to speak. Granted PEMDAS specifies a procedural method of calculation with operators; however, what is totally neglected is preciseness and elimination of possible confusion (misinterpretation of the mathematical expressions). We should teaching not just operator priority but, equally as important, procedures to prevent misinterpretation. MAKE USE OF THE "P," It is your friend and should not be neglected in use.

[@gavindeane3670]

Parentheses aren't the way to add clarity to this expression. The way to add clarity to this expression is to use a proper vertical layout for division instead of an inline operator.

[@narenmenon6906]

PARENTHESES, OR BRACKETS. One is preferred by Americans, the other by the British and consequently in India, Australia NZ, Africa, etc. This means that the result from a group of variables, usually from different inputs, must be used in a formula.

[@stevendebettencourt7651]

Okay, this is an order of operations problem that doesn’t annoy me as there is something that requires explaining, but this problem simplifies quite nicely. Sqrt(8) * sqrt(2) / sqrt(8) * sqrt(2) =? 1 First, I’m going to remind you that sqrt(x) = x^(1/2), so sqrt(x) needs to be done first. Next, notice that: Sqrt(8) = sqrt(4*2) = sqrt(4) * sqrt(2) = 2 * sqrt(2) So now we have: Sqrt(8) * sqrt(2) / sqrt(8) * sqrt(2) =? 1 => 2 * sqrt(2) * sqrt(2) / (2 * sqrt(2)) * sqrt(2) =? 1 => 2 * sqrt(2 * 2) / (2 * sqrt(2)) * sqrt(2) =? 1 => 2 * sqrt(4) / (2 * sqrt(2)) * sqrt(2) =? 1 => 2 * 2 / (2*sqrt(2)) * sqrt(2) =? 1 => 4 / (2*sqrt(2)) * sqrt(2) =? 1 Now, remember that (a*b)/(a*c) = b/c. So the 4 and 2 cancel into: => 2 / sqrt(2) * sqrt(2) =? 1 Notice that we are taking 2/sqrt(2) and multiplying that by sqrt(2). Thus: => (2sqrt(2))/sqrt(2) =? 1 Since (ab)/a = b: => 2 =? 1 FALSE So the original equation is false. However, there is a way to change the equation slightly to make it true: Sqrt(8) * sqrt(2) / (sqrt(8) * sqrt(2)) = 1 One more thing: in the original problem, we can think of it with “sqrt(8)*sqrt(2)” in a numerator and the second “sqrt(8)” in a denominator, the two sqrt(8) terms cancel out, leaving only sqrt(2)*sqrt(2), which turns into 2.

[@gavindeane3670]

This is a classic example of when NOT to follow the prescriptive order of operations sequence. Much easier to do all the multiplications and division first, and leave the power to the end. √8 × √2 / √8 × √2 = √(8×2/8×2) = √4 = 2

[@narenmenon6906]

This is why I use parentheses very liberally!!! If you write, and somebody else reads it... Life is about transmitting information accurately so that the receiver cannot read it incorrectly!

[@gavindeane3670]

The goal is to transmit information CLEARLY, not just accurately. Very liberal use of parentheses does not help with that. Nobody wants to have to read, for example, your quadratic as (a•(x²))+(b•x)+c when you could have just written ax²+bx+c Liberal use of parentheses to try and remove the possibility of misinterpretation makes mathematics cluttered and less readable, as well as being cumbersome and error-prone for the writer. Judicious use of parentheses is what's required, not liberal use. No parentheses are required at all in the example in the video. The way to add clarity here is to write division vertically, with numerator over denominator, instead of with an inline operator.

[@gavindeane3670]

​@@narenmenon6906I'm all for writing in a way that is easy to get right first time and easy to debug when it isn't right. That's why I'm not in favour of ignoring the grammar of mathematical notation and doing it all with parentheses instead. "Just use parentheses" is a common cry in the comments under these videos, but that's because the examples used to teach these grammar rules are necessarily very simple, and in very simple cases like this it is not obvious why "just use parentheses" might be a problem.

[@Stylux-z1p]

alt code for square root : ALT + 251 = √ for dot multiplication: ALT + 250 = · √8 · √2 : √8 · √2 = 1 --> false √4 · √2 · √2 : √4 · √2 · √2 = 2√2 · √2 : 2√2 · √2 2√2 · √2 : 2√2 · √2 = 4 : 2√2 · √2 = √2 · √2 = 2 --> true ------------------------------------------------------------- √8 · √2 : √8 · √2 = 1 √16 : √8 · √2 = √2 · √2 = 2 --> true

[@darkst0rm2]

Your geek skills are strong

[@charlesmitchell5841]

Well what if the problem was written as a division problem with the line separating the numerator and the denominator, then can it be seen as something divided by itself which would equal 1 ?

[@panlomito]

There is no separating line between numerator and denominator... it's only O³ with PEMDAS solution.

[@johnmarley8268]

That would be the same as putting parentheses around both sets of sqrt(8)*sqrt(2)

[@Joe_Narbaiz]

You mean using a vinculum (---) instead of an obelus (÷) or solidus (/)? If that is the case, YES. But that clearly ISN'T the case, so NO! 🤔😉😄😀😃

[@terry_willis]

@@Joe_Narbaiz Yes. That is the way I did it (incorrectly). The acronym PEMDAS needs an asterisk detailing these fine points. I should have guessed the right answer because there was a 50/50 chance AND the "correct" answer was too "obvious". This was more of a psychological question than a math question. :)

[@gavindeane3670]

If you rewrote this expression in that form (which is the normal way to write division in mathematics) then the only thing in the denominator would be √8.

[@KW-gb9cd]

√8 · √2 · (1/√8) · √2 = √2 · √2 = 2.

[@norcalovenworks]

While I see that the answer is 2, I am an engineer……and would never document my work this way. When in doubt about who your readers are, be clear. In fact, be clear for yourself, so that you don’t have to parse things out, or think about conventions……The point illustrated is a convention, not a rule.

[@gavindeane3670]

I don't think he is in doubt about who his readers are. His readers here are students learning the basic grammar rules of mathematical notation - that's clearly who the video is for. As such, he needs to use an expression which exercises those rules.

[@robinblanc8208]

Great problem!!

[@patrick3016]

So I multiplied the sqrt(2) x sqrt(2) first to get 2. Then multiplied that 2 x sqrt8) on the left to get 2 x sqrt(8). Then divided that by the remaining sqrt(8), which resulted in 2. Is this an incorrect method of doing this, solving all the multiplication values first, followed by the division values?

[@gavindeane3670]

No, nothing incorrect about that at all. What you did is completely valid.

[@chandrarai449]

Answer is 2.first of all root 2 divide by root 8 .1/2 comes.then multiply root 8 and 2 =root 16.make root 16 into square is 4.Then 4/2 =2 is answer.There is two formulas PEMDAS AND BODMAS it depends on yr country and which formula is used in your country.

[@markdevries670]

It didn't take me more than say 30 seconds to find the right answer, which is 2. 🤣 Saved me about 660 seconds of my precious time 😀

[@enriqueiii9209]

Good one LMAO

[@srjwaugh]

let X = √8 x √2 then X/X = 1

[@gavindeane3670]

That would be if it was written √8 × √2 / (√8 × √2)

[@joseluiscartesvaliente5924]

@@gavindeane3670 ¡NO! El producto no necesita meterse en un paréntesis. Esos factores YA ESTÁN "AMARRADOS" por el signo de la multiplicación. (Como en un paréntesis)

[@panlomito]

V8 = 2V2 so 2V2 . V2 = 2 . 2 = 4 4 / V8 = 4 / 2V2 = 2 / V2 = 2V2 / 2 = V2 V2 . V2 = 2 so wrong: 2 is not 1

[@sans1331]

how classic. using an obelus to represent division instead of expressing it as a fraction, because expressing it as a fraction would actually make it clear enough to interpret an answer. wow! it’s almost like people get it wrong because you purposefully made the problem as ambiguous as possible, so you get more attention on your video! who would think of that?

[@antonmilius5197]

2

[@davidwilliams1060]

Slick. I’m not to this point in your course just yet. Thanks.

[@joseluiscartesvaliente5924]

Pongamos este ejercicio, en forma de fracción. (Y llamemos "K" a raiz de 8 x raiz de 2 "raiz de 8 x raiz de 2" K .................... NUMERADOR ó DIVIDENDO (N-D) PRUEBA DE LA DIVISIÓN ---------------------------------- = -------- = UNO (1) ...... COCIENTE (C) (D-D) x (C) = (N-D) "raiz de 8 x raiz de 2" K ................... DENOMINADOR ó DIVISOR (D-D) ¡¡CORRECTO!!

[@tomtke7351]

(sqrt(8))×(sqrt(2)) ÷ (sqrt(8))×(sqrt(2)) = (sqrt(8))(sqrt(2))(1/(sqrt(8)))(sqrt(2)) = sqrt(2) × sqrt(2) = 2

[@whoff59]

@gusmath1001 ... and to use parenthesis in this case correctly mathematicians first have to know the sequence of operations used without parenthesis correctly.

[@ralphmelvin1046]

Thank you this is a good lesson now I know I understand how to multiply and divide square roots much better now thank you

[@hoonerdog]

This one got me. Doesn't the division symbol act like a fraction line?

[@drizer4real]

And that, good people of the internet , is why we use commas. ( sqrt(8) x sqrt(2/8)) x sqrt(2) ? Nobody would misunderstand that or make an error with it.

[@gavindeane3670]

It's why we write division using a vertical layout with a vinculum √8 × √2 ------------ × √2 √8

[@drizer4real]

@@gavindeane3670 👍Fair enough. As long if intent is made clear is it not ? I never understood why people would write it as stated in the video.

[@gavindeane3670]

​@@drizer4realThe purpose of the video is to teach the grammar rules of mathematical notation. That necessarily requires an example which exercises those rules. For this particular purpose, rewriting the expression in either of the ways that you and I have suggested would defeat the object.

[@doughoffman9463]

@@gavindeane3670 Yeah, what you have is better, but I would drop the 'x's because multiplication is implied. I would also add just two parentheses that enclose everything but the trailing √2. PEMDAS is once again useless.

[@patrickharley1003]

No.... Answer is 2. Liked your explanation but PEMDAS gives people the fits! 😮 Looked at problem as x multiplied by y divided by x multiplied by y. Any number y, that is first multiplied by a number x and then divided by the same number x, will still equal y. Then y multiplied by itself is the square of y. The square of a square root is just the value under the radical sign. In this case "2".

[@BrianHartman]

It didn't look right in my head when I first saw it, and I'm pretty sure sqrt(8) simplifies to 2(sqrt(2)), so I don't think it would simplify to anything a simple as an integer.

[@gavindeane3670]

√8 isn't an integer. Neither √2. The entire expression in the video simplifies to an integer though, but it isn't 1.

[@peskyfervid6515]

This is why mathematicians who want to be clear use parentheses. On the other hand, I guess no one would make a video out of it if some confusion wasn't inserted into the problem.

[@gavindeane3670]

The way to rewrite this for charity wouldn't be to use parentheses. It would be to use a proper vertical layout for division instead of an inline operator. But yea, the entire point of this is to teach the grammar rules of mathematical notation, so you need an example that exercises those rules.

[@peskyfervid6515]

@@gavindeane3670 Well, I don't want to disagree for the sake of disagreeing, but I think the point of the problem is clickbait. However, it's true writing the equation with the first half on a line overtop the second half would make things perfectly clear. Maybe the point of the video was to say, "Don't write equations this way if you want correct answers."

[@gavindeane3670]

​@@peskyfervid6515No, the point of the video is to teach the grammar of mathematical notation. It's tempting to look at it and think of ways to make it clearer, but that misses the point. To teach the grammar rules you need an example that exercises the grammar rules. But of course it also needs to be a very simple expression so that the students can easily understand what's going on. Because the examples used to teach these rules are necessarily simple, it's almost always the case that one or two sets of parentheses could make the whole issue go away without impacting clarity, and so there's always a few people in the "just forget those rules and use parentheses" camp. But that wouldn't work well in the real world, where mathematical expressions are not always as simple as this.

[@peskyfervid6515]

@@gavindeane3670 I agree that mathemativcal expressions can be very difficult, but surely the purpose of mathematics is to arrive at a correct answer? Surely the reason to use braces and brackets in mathematics is to clarify difficult equations? Why else would they be there?

[@gavindeane3670]

​@@peskyfervid6515No, the purpose of brackets in mathematical notation is to indicate that what's enclosed in the brackets is a single, inseparable thing - such that you cannot perform operations on just part of it, you can only perform operations on all of it. I know that they can be used to aid clarity, and that's fine, but that is not why they exist. They could be used to add clarity here if we are keeping the expression inline. But as general idea, ditching the precedence grammar in mathematical notation and doing it all with parentheses instead would be a mess. Nobody wants to have to read, say, a quadratic written as (a•(x²))+(b•x)+c when it could just be written ax²+bx+c

[@randallheisey3698]

The answer is 2.

[@joseluiscartesvaliente5924]

PUES SÍ. Eso de PEMDAS es una MIERDA, no contemplada en la Aritmética. En Aritmética, hay un PRINCIPIO MUY CLARO: A : A = UNO (1) Y ese A, puede ser CUALQUIER NÚMERO, como por ejemplo, "Raiz de ocho x Raiz de 2"

[@russelllomando8460]

NO it's X then / then X cute... thanks for the fun.

[@calvinmasters6159]

I can see how if someone is a hairdresser, or an dance instructor, they can get by without this stuff, nor even see a reason for it.

[@nfpnone8248]

Even the way you read the problem was incorrect, because the way you read it everything to the left of the division sign is the numerator and everything to the right is the denominator, and you reinforced that by underling them to group them as a numerator and a denominator! The reality is everything is in the numerator except the square root of 8 which is in the denominator, which cancels with the square root of 8 in the numerator leaving the square root of 2 squared which is 2. Sorry PEMDAS does not apply for this equation, and let me make a suggestion to you, learn the difference between fixed and implied operators!

[@gavindeane3670]

This is not an equation, it's an expression. Anyone with the level of mathematical knowledge you claim to have would not make that mistake - but then, we all know you do not actually possess that much knowledge. PEMDAS works absolutely fine here, as it does with any expression made up of the operations and notation that PEMDAS covers. That is the entire point of it.

[@Surreal_Wizard]

No, Mister Youtoube Math man. Hoochie 8 times hoochie two dividied by hoochie eight times hoochie two does not equal one.

[@darellpiper7227]

NO, the answer is 2

[@profdimateonline]

Hi colleague, very nice channel 👍I have a math channel too. Greetings from Italy 😊

[@Rogan-p6m]

I simply did: √(8×2-8×2) and came up with the right answer, am I nuts? 😭

[@Motagee651]

This guy is good. He breaks it down and makes it seem so simple. Where was you when I was taking math in high school and college? I could have went on to Calculus ! 😂🤣😂🤣

[@robertlevasseur6843]

This is why I hate math. Math teachers spend most of their time trying to trick you and explain why you are wrong.. How about telling us what practical use an equation such as this one has in the real world. Maybe that way the fact that the answer is 2, not 1 would matter.

[@gavindeane3670]

That seems an odd request. The subject matter of this video is not solving a particular problem. It's more elementary than that - it's teaching the basics of the language. Understanding the language and grammar of mathematical notation is relevant to EVERY practical use of mathematics. In order to assess the relevance of this, the win you should be asking yourself is not, "do I need to be able to evaluate √8 × √2 / √8 × √2?" The question you should be asking yourself is, "do I need to be able to read and write mathematical expressions?"

[@chrisdissanayake6979]

Answer: yes it is correct. But, following PEMDAS, going from left to right, it is wrong. ------------ √8 x √2 ➗ √8 x √2 =1 Any number divided by the same number equals 1. Then, it is correct. ----------- But, following PEMDAS, √8 x √2 ➗ √8 x √2 √16 ➗ √8 x √2 √16 ➗ 2 √2 x √2 4 x √ 2 4 -- -- = --= 2 2 √2 1 2

[@panlomito]

(V8 . V2) / (V8 . V2) = 1 But that is not what is asked here.... (V8 . V2) / V8) . V2 = 2

[@whoff59]

Evaluation is from left to right. But do *not* group the single parts differently using parenthesis: that changes the sequence of operations.

[@mayaq8324]

12 minutes wasted

[@whoff59]

a*b*c*d = a*c*b*d (commutative law) and ÷x is the same as * (1/x) Therefore you can write the term as sqrt(8)÷sqrt(8)*sqrt(2)*sqrt(2) evaluate from left to right: sqrt(8)÷sqrt(8)*sqrt(2)*sqrt(2) = (sqrt(8)÷sqrt(8)) *sqrt(2)*sqrt(2) = 1 * sqrt(2)*sqrt(2) = 2

[@FreeFlyerUk]

Isn't the correct answer plus OR minus 2?

[@gavindeane3670]

No. √8 is positive and √2 is positive. That's the definition of the √ symbol. If you want to refer to both square roots you write ±√2, but the author hasn't done that here.

[@narenmenon6906]

NO. √2 ÷ √2=1 (-√2) ÷ (-√2) also equals 1

[@thenetsurferboy]

Answer is 1 You solved and you effectively wrote [Root 8 x root 2 x root 2 ] / root 8 So two expressions according to you give the same answer, the other one being, root 8 x root 2 divided by root 8 x root 2 You do not understand Pemdas or Bomdas I am trying hard to avoid any more of this

[@gavindeane3670]

You do not understand PEMDAS/BODMAS. The expressions √8 × √2 / √8 × √2 and √8 × √2 × √2 / √8 are equivalent. No idea why you would be surprised that two different expressions can mean the same thing. That's completely normal. Almost any mathematical expression can be rearranged in this manner while preserving the meaning, provided that you understand the precedence and commutativity and associativity rules.

[@thenetsurferboy]

@@gavindeane3670 But they are not the same Do not worry When you are promoted to grade 4 next year you will not see this drivel again

[@josephlaura7387]

No

[@geogeo6071]

Put some parenthesis in the right places and make an unambiguous expression that will make it mean what you intend, then you don’t have to mess with this PEMDAS bullshit. No mathematician worth his salt would write an expression like the one you wrote.

[@gavindeane3670]

No mathematician worth his salt would suggest ditching the concept of precedence and doing it all with parentheses instead. That would make mathematics basically unreadable. You may have heard it is as a suggestion - it comes up quite often in these comments threads. But it's only ever suggested by people who have no idea what the actual implications would be. "Just use parentheses" is not a serious option.

[@geogeo6071]

@ you’re ignorant

[@geogeo6071]

@ you’re ignorant

[@carlabennett9513]

Yes

[@Joe_Narbaiz]

No, it's not.

[@gusmath1001]

Totally idiotic problem! There is a reason mathematicians use parentheses.

[@georgemacarthur6875]

No

[@georgemacarthur6875]

Yes

[@sandrasimpson1314]

1

[@rodfulford4306]

2