The square root of 27 divided by the square root of 50=? Basic Algebra!

[@thecalculator80]

Root 27 is a little more than root 25 which equals 5. Similarly, root 50 is a little more than root 49 which equals 7. So the answer is near 5/7. Answer b) is the only answer less than 1.

[@robertloveless4938]

Quit being logical. I was taught (MANY years ago) to 1st eliminate the impossible. Coincidentally, that's whaf Sherlock Holmes said to do.

[@thebasisti2482]

Yeah

[@tuncayvsran3116]

B

[@Alo-n7l]

27

[@Ghredle]

Exactly my first aproach

[@hraydetective]

As a 74 year old former English major who had a career in IT I didn't need the coaching on test-taking, but the explanation on how to derive the answer algebraicly was worth the viewing.

[@billh5923]

I fairly quickly did it in my head. Can't believe it took a 20-minute video to explain this simple problem.

[@richardhole8429]

Note that this view has been seen by 179K people. How many on your channel?😢

[@natashabacevic7599]

Me too, needed a minute in my head. Ridiculous

[@nickfraser4599]

Not everybody is as facile as ye and me! The video is really for them as is not. But if they practice enough they will become so. Cheers!

[@PaulEEish]

I'm a tail-end baby boomer/gen X and was always a B+ or A- student in middle and high school and had to work hard at math. I am convinced that had I had a tutor like you (and YT) back then, I would have aced my math courses consistently. Nevertheless, because it's never too late to learn, I'm relearning basic math skills. Why, some might ask? It's because it gives me great joy to master what I know I can, reinforces what I already know, and keeps my mind sharp.

[@YAWTon]

The result is less than 1. This rules out a, c, and d. So the answer is b. To evaluate multiply by sqrt(2). This leads to sqrt(54)/10, which is the same as 3×sqrt(6)/10. The only thing that is difficult is how to make a 20 minutes clip out of a trivial problem...

[@starblue3598]

I passed Algebra 2 in high school by guessing and eliminating wrong answers on multiple choice tests. ( teacher was too lazy to actually look at your work). Now I watch your channel to understand what I never did. (73 years old).

[@geneloscowski3070]

I've been teaching advance math for 42 years. I've never seen such a complex solution to a simple problem!!!

[@dough9512]

Complex?? Do you actually mean "time-wasting"?

[@johnshaw6702]

I'm curious. What method you would use to prove that (b) was the correct answer? Although it is simple to assume (b) is correct, through logic, as he mentioned in the lesson, but in real life you don't have multiple choices given to you.

[@davesutherland1864]

I agree. Lots of people have posted correct solutions that you can read in 30s. Even if you have to think about what they write a bit it should still take less than a minute to follow the logic.

[@Kualinar]

I start with a quick approximation. ✓27 is a bit larger than 5 (✓25), and ✓50 slightly larger than 7 (✓49). So, the result must be less than 1. The ONLY proposed answer that is less than 1 is (3✓6)/10, or about 0.735, (B). Many years ago, I solved a LOT of similar problems in my math classes. Thanks for the refresh.

[@philipkudrna5643]

Sqrt(27) is 3*sqrt(3). Sqrt(50) is 5*sqrt(2). If we rationalize the denominator by multiplying with sqrt(2) we get 3*sqrt(2*3)/ (5*2) or 3*sqrt(6)/10 or answer b)

[@keithclancy1537]

I don't think I ever had a Math teacher give multiple choices with only one possible answer. The numerator is smaller than the denominator therefore the answer is less than 1 only one choice has any possibility of being less than 1.

[@robertloveless4938]

You'd be surprised how little common sense is emphasized in school anymore.

[@jeffreyfoster8413]

The problem I have with multiple choice tests is life isn’t multiple choice. They just made it easier for teachers to grade.

[@zembalu]

Since this is a multiple choice question, it is trivial, because the result must be less than 1.

[@cosimo7770]

Mental arithmetic in 2 seconds shows it is (b), because only (b) is less than 1. Maths teachers should teach insight, not absurd mechanical rules.

[@gordonspond]

Agree

[@highpath4776]

@@gordonspond but if all answers were

[@johnshaw6702]

OK. e) None of the above. Now are you as sure of the answer? The rules give you the base from which to build understanding. Understanding leads to insight. This is a video that teaches mathematics. He explained how you determine that the answer of (b) is the correct answer, but that is actually an assumption.

[@Kyravexa]

Took your way at first, got stuck at 11:22, then decided to take another step and expanding (hope that is the correct english word) Root27/Root50 by Root2 and got Root54/Root100 = Root54/10 = Root(9*6)/10 = 3*Root6/10, means b) is the correct solution

[@nickfraser4599]

Take the squares out of each you end up with 3✓3 / 5✓2. Now multiply by ✓2/✓2 ( since that is one and you can get multiply anything by one and get away with it! ) and you end up with 3✓2✓3 / (5 *2) or 3✓6/10

[@mata2723]

yes, the video explanations is so long for just this....

[@ianwilson9716]

I appreciate the way he looks at possible misunderstandings then explains the various options, which leads to a deeper understanding

[@troglokev]

So that’s 3 root3/5 root 2. Multiply top and bottom by root 2 to get 3 root6/10. b. Not sure why this takes 20 minutes.

[@b213videoz]

Thanks to this American I can now solve these kind of problems (a few months ago I couldn't)

[@timmiddleton9227]

Dude, thanks anyway, but I died & was buried waiting for you to solve it. Geez, we are mortal after all.

[@Shay-q8u]

enjoy being at best a d student then.

[@johnshaw6702]

Thanks. I came up with the presumption that the answer was (b) because √27 < √50, and would have chosen that on a timed test. At 64 I rarely do math and got as far as (9 x √3)/(5 x √2) in my head, but decided that was enough mental excercise without writing it down. So I watched the video instead. You did a good job of expainig how to prove that the presumption was correct. I said "presumption" above because of the fact that without proof you are only assuming that one of the given choices is correct. In other words, you are making an educated guess, because the answer must be less than 1.

[@geogeo6071]

Not allowing square roots in the denominator is purely a matter of style.

[@highpath4776]

but it makes it easier ? to compute an exacter number - the trick to multiply by a suitable substitution for 1 is something I would not have thought of

[@kuplace1984]

Excellent class. Excellent job. Very knowledgeable in Math. Easy to follow and understand. Your chanel is a great resource. Thank you.

[@AlfredBasso-z7h]

I solved this in a second realizing that the answer would be less than 1.

[@chrisjohngrima9761]

I don't if anybody had already said this but you could have done Sqrt(27)/sqrt(50) = sqrt(27)*sqrt(50)/sqrt(50)*sqrt(50) Sqrt(1350)/50 = sqrt(9)*sqrt(25)*sqrt(6)/50 Sqrt(9)*sqrt(25)*sqrt(6) = 3*sqrt(6)/10 Explanation: If your denominator is a root, you to get rid of the root without changing the value. For the first step, you can multiply the numerator and denominator by the sqrt(50) (Note that you can't sqaure both sides because that would give a different number eg sqrt(2)²/sqrt(3)² ≠ sqrt(2)*sqrt(3)/sqrt(3)*sqrt(3) ) After multiplying both by sqrt(50) you should get sqrt(50)*sqrt(27)/50. Our next step is to combine both root in to one root which would be sqrt(50*27)/50 = sqrt(1350)/50 After this, we should find the prime factors of 1350. Which is 1350=2*(3^3)*(5^2) Now we are only interested into getting the square numbers, now one of them is 5^2 but another one is 3^2 meaning we can rewrite this as 1350=6*(3^2)*(5^2) Which means, sqrt(1350)=sqrt(6)*sqrt(9)*sqrt(25) Because our denominator is 50, we can divide both side by the sqrt(25) giving us Sqrt(6)*sqrt(9)/±10 Next is to find the sqrt(9) which is ±3 So now our eqaution is, ±3*sqrt(6)/±10 Because there is ± both on the numerator and denominator we can cancel it out. Making our final answer, 3*sqrt(6)/10

[@gavindeane3670]

That's impressively complicated (and you can drop the ± stuff as there's no ± here). Giving yourself the task of finding the prime factors of a number like 1350 when you can just see from inspection that 27 is 3×3² and 50 is 2×5² is a good one 😂

[@Valerie-ek5ly]

Thank you for another great video. Very well explained, and touching base on every step!

[@Surreal_Wizard]

Three-hooky thing -six on top of the horizontal bar, ten underneath

[@harrymatabal8448]

Mr joseph. I agree with you 100%. Have a great day and may god bless you for helping math learners.

[@robertstuart6645]

The hardest part of doing this problem is rationalizing the denominator. By applying the laws of radicals, the answer is simply (3x3^,5)÷(5×2^,5).

[@lukeknowles5700]

I guessed the answer by approximating the original two square roots, and then comparing that estimate to the four choices of answers. Only one of the four could have been close, so although I forgot the details of solving this, I was confident just using approximations. But now I know how to solve it precisely!

[@sharocooper669]

Sqrt of numerator is smaller than sqrt of denomator; b is the only answer that fits..

[@borstenpinsel]

27 < 50, since both are >1 this means sqr27 < sqr50 which means the 0>result>1 which rules out all but b)

[@flagmichael]

... or "none of the above." Welcome to YT math.

[@calvinmasters6159]

Fun. For once I didn't guesstimate first, but looked for factors in the original question. They just looked factorable. Once I had 3 root 3, and 5 root 2, the rest was just picking up the pieces.

[@TheAZZA0990]

Really quite straightforward! b !!!

[@erembald2927]

Not too sure about this bur here goes: 27^0.5/50^0.5 = (9^0.5 x 3^0.5)/ (25^0.5 x 2^0.5) = (3 x 3^0.5) / (5 x 2^0.5), multiply the square root components top and bottom by 2^0.5 = (3 x 6^0.5) / (5 x 4^0.5) = 3 x 6^0.5 / 10

[@haraldreimann-trusheim2993]

why do i need to calculate anything? 27 SQRT(27)0) => SQRT(27)/SQRT(50) < 1 b) is the only solution 3*SQRT(6) < 9) Just 30 seconds to solve, because this is multiple choice

[@icespeckledhens]

Very good explanation, thanks

[@chrisdissanayake6979]

This is his KZbin channel. So, we can’t be rude, picking on his style of teaching. Each of our minds are unique and each one operates the way it has been programmed and maybe according to the genes too. We have an advanced human brain to realize that and let’s be appreciative of what we are offered in life. Maybe there are some others who are not that smart as you all who complain, and they must be learning and benefiting from the hard work of this teacher. It is impossible to please everyone, when it comes to anything in this world. Maybe you all can have your own channel to display your expert math skills!

[@Shay-q8u]

Numerator: 27 is just 3 * 3 * 3 Denominator: 50 is just 5 * 5 * 2 Numerator is 3(3^1/2) Denominator is 5(2^1/2) we have a root in the denominator so we multiply: Numerator: (3 * 2)^1/2 gives us 3(6^1/2) Denominator (2 * 2)^ 1/2 5(4 ^ 1/2) is 5 (2) which is 10 Final answer [3(6 ^ 1/2)] / 10 This is answer b since 1/2 as exponent means square root.

[@bravikumar8950]

Good explanation 👍👍

[@jetman551]

In John's defense, I needed to see the whole process. Now I get it.

[@rcnayak_58]

Let us do it in a very simple way. The question is √27/√50. We can write it as √ (27/50) which also equal to √ (54/100). Let us convert all possible answers in this form. (a) 5√8 = √ 25. √8 = √ 200. (b) 3√6/10 = √9.√6/√100 = √(54/100) (c) √ 1350 (d) 8√6 = √ (64.6) √ 384. Clearly, the answer is (b).

[@ChaosPod]

Break each number into their prime factors, 27 = 3^3 and 50 = 2x5^2, so sqrt(27) = 3 sqrt(3) and sqrt(50) = 5 sqrt(2), then rationalise the denominator by multiplying by sqrt(2)/sqrt(2) and you’re done.

[@LouisHansell]

Correct answer can be seen at a glance of the choices. Square root of 27 is ~5, of 50 ~7. So the answer should be around .7, 5-7ths or ~5x.14. Answers a, c and d are too big to way-too-big. So only answer b remains. On second glance, you can see that answer b is 3/10 of square root of 6. if that was SR of 4, 2x.3 = .6. Close enough to .7. So you can get the correct answer easily.

[@harrymatabal8448]

Excellent John sir thanks for telling us that you are teaching for s decade. Do you know that 1year experience multiplied by 10 is not the same as 10 years experience multiplied by 1.

[@ericlipps9459]

It's (b). sqrt(27)/sqrt(50) = sqrt(27/50)=sqrt(54/100). Not take sqrt (1/100) outside the radical and you have sqrt(54)/10. 54 = 9*6, so you can take sqrt(9)=3 outside the radical. Now you have 3 sqrt(6)/10. Q.E.D.

[@shakkazulu4237]

The answer is 3/5

[@yingxinsun1870]

The answer is obviously less than 1, so only B is possible right

[@OuryLN]

It’s more that one forgets these rules since we don’t often use radicals and just simplify and estimate

[@russelllomando8460]

got it B took some factoring & reducing thanks for the fun

[@Cccoast]

Is it weird that i love these problems ?

[@rhigel2269]

Yes!

[@moboutmen]

My sixth grade teacher would have killed me if I got this wrong, 55 years later!

[@caraswintelski4106]

Dear Mr Tablet I like to do two of these in the morning. I CANNOT spend 40 - 50 minutes doing this. PLEASE cut the running times in half or do two versions. Thank you. Dr S.

[@davereynolds739]

He always gives the correct answer at the beginning of his videos. If you get the correct answer, just don't watch the rest of the video.

[@Rick_the_chemist]

When a number is divided by a larger number, the answer is always less than one. Answer b is the only option less than one, so it is the correct answer. Simple logic.

[@deltalima6703]

Thats how I got it but it seemed sus. Ran it through a calculator, and sure enough. Then realized 27 is 9 x 3 (god, idiot!) and the entire method was clear to me. Embarassing a little, so I gave him a thumbs up and watched the video as punishment. :)

[@argonwheatbelly637]

Just rationalize the denominator, factor, and reduce. Pretty simple.

[@rdspam]

It’s roughly 5/7 and only one answer choice isn’t >1.

[@mrblakeboy1420]

the answer is obviously less than one, and three of the options are obviously more than one, but i’ll prove it anyway. it’s 3sqrt(3)/5sqrt(2), which is 3sqrt(3/2)/5. multiply both parts by 2(put the 2 in the square root) and you get 3sqrt(6)/10, which is answer choice b

[@andyl8055]

Could only be b. The others are all greater than one.

[@flagmichael]

You did okay - a little long but you were taking the scenic route - up to 17:00. That was all you needed to do. Getting the radical out of the denominator is fine, but then why did you leave it as a fraction rather than converting it to 0.3 sqrt 6? A matter of taste, I suppose.

[@Sailor376also]

It can only be (b) It is about 5 divided by 7,, a value less than one. (a), (c), and (d) all have values greater than one.

[@richardhole8429]

My method also.

[@dougnettleton5326]

A great way to look at it, but I never assume that any one of the choices is necessarily correct. So, while it couldn't possibly be a), c), or d), I checked that b) was, in fact, the answer. I didn't watch the video because I don't want to know how a three step solution could take so long to explain: sqrt(27)/sqrt(50) => 3×sqrt(3)/(5×sqrt(2)) => 3×sqrt(3)×sqrt(2)/(5×sqrt(2)×sqrt(2)) => 3×sqrt(6)/10

[@Sailor376also]

@@dougnettleton5326 I like your method. Yours made immediate sense. I am a nuts and bolts kind of guy,, quadratic equations are not my thing.

[@starman2337]

If Sqr Root of 2 is an invalid denominator, how can you multiply by a number with Sqr root of 2 in the denominator?

[@rezamohamadakhavan_abdolla8627]

Thank you very much

[@ddemoon-y3w]

What's your number for a week maths lesson

[@ccw8401]

never mind. You answered my question when I watched the video.

[@johnnyrosenberg9522]

I didn't watch the video since it's over 20 minutes long. Here's my try, though: ✓1350 is definitely wrong. I can see an easy way to get 10 as denominator, so let's try that: ✓50=✓(100•½)=10✓½ ✓27=✓(3•9)=3✓3 (or, if you'd rather prefer, ✓27=✓3³=✓(3²•3¹)=3✓3) (3✓3)/(10✓½)=3✓(3/½)/10=3✓(3•2)/10=(3✓6)/10, so B it is. Now, looking at A and D I realize that I should have had a look at those before beginning to calculate, since they are both impossible answers to this question, but calculating is one of the fun bits in maths anyway, so I'm OK with that.

[@Laneboy007]

Would of been interesting if one of the answers was say 2.7^2 instead of all but one of the answers being over 5

[@MichaelGozum-ny9ne]

sqrt(27/50)=sqrt(54/100)=sqrt((9*6)/(100))=(3/10)*sqrt(6)

[@NMalteC]

😅I don't know how to solve this mathematically but given a multiple choice option, it's clear that only b) comes close enough to my thinking which is sqr 27 is about 5, sqr 50 is about 7, 5/7 is about 0.7. Close enough to get the answer right using logic and a bit of arithmetic

[@panlomito]

An irrational in the denominator... V2/V2 will eliminate that culprit... V27 / V50 = 3V3 / 5V2 = (3V3 . V2) / (5V2 . V2) = 3V6 / 10

[@shakkazulu4237]

The answer is 3/5

[@tomekdluzniewski2085]

If we assume that one of the answers is correct, then the only one that is less than 1 is b, as is √27/√50

[@sie_khoentjoeng4886]

Since √27 < √50, then √27 / √50 < 1, and the only answer that less than 1 is 3√6 / 10 (before I start to count it)

[@koenigal]

Answer B: factor out the squares 9 and 25, then multiple top and bottom by the square root of 2, and you get answer B

[@skipbrewer8101]

3√3/5√2 gets the same answer. I will watch video for further simplification.

[@tonywardle1140]

Like what you are trying to do...but found myself saying "just get on with it" Too repetative...

[@jamav8r]

He does tend to ramble a lot

[@tamptus3479]

a c d are integer in some algebraic field sqrt(27) / sqrt(50) is never in integer so b is the only possible answer

[@TheAZZA0990]

To be or not to be?!! b of course!! :)

[@Ron_DeForest]

Don’t make a big square root. Break down the top and bottom to 3 root 3 / 5 root 2. Rationalize the denominator then bring to lowest term. Way faster.

[@RustyWalker]

B, estimating with the roots of 25 and 49.

[@bigdog3628]

and that is why you should never have multiple choice in mathematics.

[@RustyWalker]

@@bigdog3628 Especially when only one is possible

[@shakkazulu4237]

The answer is 3/5

[@shakkazulu4237]

The answer is 3/5

[@glennmccarthy4264]

B is the answer after you rationalize the denominator.

[@gerardfojas7693]

b) 3 SQRT (6) / 10 is the answer

[@jackieadams6116]

Mr Math Man racialize with just •1, I’m never gonna forget how to rationalize the numerator or denominator. I want forget one.

[@rubenfuentes205]

b). 0,3 √6

[@windy7259]

Easy: SR27 is 3SR3, and SR50 is SR100 divides by SR2. Thé result is so 3SR3 divides by SR(100 /2) , that GI es: 10/SR2, resulting in thé second solution.

[@ramsinghbora1655]

Skipbrewer,pls rationalize the fraction which will come 6/10*_/6

[@bigdog3628]

√27 is 3√3 √50 is 5√2 we can't have a √ in the denominator so multiply top and bottom by √2 numerator is 3√6 denominator is 5 (2) or 10 Can't reduce further so (3√6)/10 is the answer.

[@normhardy]

The only option that makes sense is b. It is less than 1, which is clear from the original question.

[@shakkazulu4237]

The answer is 3/5

[@robertgraybeard3750]

All the answers except (b) are clearly larger than one while the answer must be smaller than one. I had to watch the video to remember the "trick" of getting to (b).

[@aljjeeran]

b)3square6over 10

[@bobbresnahan8397]

3/5/square roots 3 + 2

[@robertstratton1838]

Easy to answer since it has to be less than 1 a fraction. None of other answers are less than one.

[@murdock5537]

√27/√50 = 3√3/5√2 = 3√6/10

[@MimiMimi20_09]

I’m so glad I was not one of your students not sure why you go around and around to explain how to find the solution 🙄

[@gordonspond]

Since the answer is less than one, 3 of the possible answers can be eliminated without doing any algebra.

[@ramesankd1604]

5.3.14

[@jayantabanerjee6864]

Option 'b' is correct

[@shivanandaaithal4818]

Simple calculation the answer is less than 1. So b is the answer

[@pandurangaraonimmagadda9966]

3. Root of 3/5 root of 2= (3.root 3.root 2)/(5.root 2.root 2)=(3 root 6)/10 , So answer is😅 (b)

[@EricWells-s2p]

Two steps, only. 3^6/10

[@TH-1207]

Wow you sure went through a lot more steps than necessary. You were almost done when you had the fraction under the radical. Here you multiply the numerator and denominator by 2 and then take it back apart so the denominator is sqrt of 100 and numerator is sqrt if 54. The numerator then factors into 3 time sqrt 6 and denominator becomes 10. The hint for this approach is in the answers. 50 is half of 100 and 10 is the sqrt of 100. Actually just recognizing this lets you know that (b) is the only correct answer.

[@shakkazulu4237]

The answer is 3/5

[@barney2001]

multiple choice. you don’t solve the problem, you eliminate answers that it couldn’t be.

[@Shay-q8u]

this is exactly why in my country you NEVER have multiple choice in Math unless show your work is required. I actually had a challenge for my class once when they begged me to have a multiple choice test. I told them I would do one, but they would have to show each and every step NOTHING in there head. In exchange any student who got the questions 100% right would have their grade raised a full letter and anybody who got even one wrong answer would have their grade lowered one full letter. To be fair the test was optional and they did NOT have to take my challenge. All of them accepted though. I threw a curve ball on one of the questions and did NOT have the proper answer listed. Only 2 students of a class of 18 got their grade raised everyone else didn't even come close to getting it and I did NOT need to throw the curve ball.

[@shakirhamoodi5009]

b) 3 sqrt(6) /10 It took me one minute

[@mylittlepitbull3143]

How to make a simple problem hard.

[@shakkazulu4237]

The answer is 3/5

[@maxinemcafee4893]

Got b. Wow got it right!

[@bjorneriksson6480]

I did not understand why you could not have an irrational number as denominator?