It has been over 40 years since I encountered that sort of problem Thanks for the refresher.
@nyneeveanya88618 ай бұрын
Well got half way through and thought I was done. I forgot about the IN in the denominators rule. So cool when I’m nudged awake again. Thankyou!❤
@petervankessel87418 ай бұрын
Split the quotient: 27^(1/3) * (1/16)^(1/3). 16 can be written as: 2 * 8. That means: 3 * (1/(2 * 8))^(1/3). 2^3 = 8. That means that the cube root of 8 is 2. So, the equation can also be written like: 3 / (2 * 2^(1/3)). Or: (3/2) / (2^(1/3)). Or: 1.5 * 2^(-1/3).
@petervankessel87418 ай бұрын
That is rounded 1.19.
@jeffreyleonard72102 ай бұрын
That is what I got
@kssrinivasan9778 ай бұрын
Explanation is too much
@dave9298 ай бұрын
I got the answer in about 10 seconds.
@margaretcorfield98918 ай бұрын
Dozed off in the middle bit. Knew the answer anyway.
@jamesharmon49948 ай бұрын
It is far better to explain too much than too little.
@Ron_DeForest4 ай бұрын
That’s the point of the channel.
@Ron_DeForest4 ай бұрын
@@dave929 Congrats. I’m always on the lookout for the I did the question in nanoseconds. Here you are. Thank you for making the search easy.
@dragondog31808 ай бұрын
I prefer the result 3/(2*cuberoot (2))
@monetary017 ай бұрын
That's exactly what it should be
@mikem65493 ай бұрын
yep me too 16=8*2 yeilding 2*cuberoot(2)
@jeffreyleonard72102 ай бұрын
Ah! Cannot have an irrational number in the denominator
@ESeth-xb5cu2 ай бұрын
It’s 3/2*cbrt(2)
@NikiokoАй бұрын
That's not the final answer.
@russelllomando84608 ай бұрын
great one. only missed the final factor. always fun though. thanks.
@MrSeezero7 ай бұрын
You all can look at it this way. When you have an a^(1/r) in the denominator, you need to give this term r-1 identical "buddies" and then put a copy of each of those "buddies" in the numerator to work toward the proper radical format when presenting a value as an answer. If it is a square root, you need one (2 - 1) "a^(1/2)" in both the numerator and denominator. if it were a seventh root then you, of course, would need six (7 - 1) "a^(1/7)"s in both the numerator and denominator.
@Valerie-ek5ly3 ай бұрын
Thank you so much. Another excellent video! So correct about textbooks not teaching this!
@raelik7778 ай бұрын
I would have first simplified it as: 3*cube_root(1/16) using the multiplication property of radicals, reading 27/16 as 27 * 1/16. Then you can reduce cube_root(1/16) by using the equivalent fraction 4/64, and the division property of radicals to get 3*cube_root(4)/4
@Astrobrant24 ай бұрын
Cube root of 4/64!! I never would have thought of that. Great stuff! Thanks.
@samswift49212 ай бұрын
1.2 if rounded to one decimal place.
@proteus4046 ай бұрын
I didn't know how to rationalize a cube root denominator before watch your solution I was looking for ways to solve it this is what I thought the cube root of 16 is 16^1/3 so if I times both numerator and denominator by 16^2/3 it would leave 16^3/3 so just 16 3x 16^2/3 = 3 x cube root 256 3 x cube root of 64x4 3x4x cube of 4 / 16 3*Cube root 4 / 4 Your way is much easier
@egaydemesa53534 ай бұрын
3/4 (cube root of 4)
@olenfersoi88877 ай бұрын
It would make more sense to, in the last step, multiply by the cube root of 2 over the cube root of 2 twice...effectively cubing the cube root of 2 in the denominator to give 2; then simplifying the 2 cube roots of 2 in the numerator to the cube root of 4.
@TheSharma111111Күн бұрын
With all my respect your explanation make students loose track off the main subject
@Astrobrant24 ай бұрын
I got part way through doing this in my head and saw your cube root of 4 in the answer and said, "What the ...???" I was thinking of just multiplying the cube root of 2 times the cube root of 2. But I was wrong, as you showed. Doing that will still leave a radical in the denominator. Oops! Good problem and good explanation. But please try not to repeat yourself so much. You explained the 7/√3 example three times.
@dmp044 ай бұрын
That's where I made my mistake.
@michaelhutson67587 ай бұрын
What's wrong with 3/2 × ∛(1/2)?
@monetary017 ай бұрын
That will be too easy for him and not enough time wasting!
@ZINGYWINGYASMR4 ай бұрын
Thankyou sir ! denominator rules 🙏
@mathmandrsam8 ай бұрын
What are your thoughts on (3 x 2^(2/3)) / 4?
@user-ri6rn7ti5h8 ай бұрын
My thoughts precisely too
@quigonkenny7 ай бұрын
The way I've seen it in classes and on these math channels, is they tend to frown on having fractional exponents in the final answer, or exponents in the radicand, unless logistically necessary (ie: if it's more feasible to express the radicand as an exponentiated term rather than a rational number). Thus ∛4 is more ideal than 2^(2/3) or ∛2², but ∜71³ would be preferable to ∜357911.
@Loonypapa8 ай бұрын
Did this in my head.
@silverhammer77798 ай бұрын
3/2 x (Cube Root of 1/2)
@jamesharmon49948 ай бұрын
Yes, but rationalize the denominator.
@silverhammer77798 ай бұрын
@@jamesharmon4994 Why? I have run into many equations used in engineering and science that have radicals in the denominator. If it's good enough to design bridges and spacecraft, it's good enough for any Real World application.
@sloth617 ай бұрын
@@silverhammer7779 That bridge will not stand very long with a rational in the denominator.
@aryusure19436 ай бұрын
Well explained! I got to 3/the cube root of 16 but I knew it was not enough. Repeat after me, we can't have an irrational number as the denominator. :( Got it! Thanks!
@SM-ev3pv8 ай бұрын
Many will get this wrong! How many? You must have really blessed students.
@monetary017 ай бұрын
I'm astonished at the number of people watching his very basic videos. I do it as a research for viewing statistics myself.
@earnesta.brooks71237 ай бұрын
This is simple: 27 is 3 cubed. And 16 is the cube of 2 : ( 3x3x3)÷ (2×2×2) So the cube root is = 3÷2 = 1.5
@dmp044 ай бұрын
16 is 2 cubed x 2. 8 is the cube of 2.
@BillGraper7 ай бұрын
My math OCD doesn't like cubes in the numerator. I'd still like to solve it, as it seems like it doesn't have a "true" final answer. It would have a decimal that never ends, most likely. 🤔
@fernandobriseno81647 ай бұрын
Takes me back to my highschool days.
@kennethstevenson9768 ай бұрын
This problem is easier if you use fractional exponents and rationalize the denominator.
@NikiokoАй бұрын
3 / (2 ⋅ ³√2) = 3 ⋅ ²√4 / 4
@subasu4782 ай бұрын
3/2squre root 1/2
@danrodde73166 ай бұрын
What is the program that John uses to both have typed problems that he can write over and the hidden pen to write with? It looks like a Mac program.
@philipwebb82977 ай бұрын
Thank' !
@deograciousuwiragiye84297 ай бұрын
Cubic of 2×3/2
@jvolstad7 ай бұрын
I didn't get it right at first, but I understand your explanation. I am a 71-year-old senior citizen student at my local community college, with a 3.9 GPA. 😊
@mollymam71538 ай бұрын
(3cubed root of 4)/4
@victorjacob1413Ай бұрын
Answer 1.5
@GaryBricaultLive5 ай бұрын
Actually 1 1/2 * ((1/2)^1/3) is not an invalid answer. Just because this guy chose to leave the radical in the denominator doesn't mean that it had to be removed in other solutions to the problem.
@richardhole84293 ай бұрын
It is standard practice to remove radicals in the denominator, and your math teacher may reject your answer, not as incorrect but as being incomplete.
@user-ny4og2rq4j2 ай бұрын
try that in my class I'll sneer at you and mark the whole question wrong. You NEVER leave a root in the denominator! Even my D- students know that.
@jeffreyleonard72102 ай бұрын
These need to be 7-8 minutes in duration
@landixable7 ай бұрын
1.5
@bestdroidgames75034 ай бұрын
Why didn't you divide the square root 4 to get 2. Thanks answer
@thomassidoti5496Ай бұрын
becaue then you would have to do that to the numerator and that would cause chaos
@user-yk8hf2hb2x7 ай бұрын
i wonder how many of his students fall asleep from boredom because he takes forever to get to the solution to the problem.
@bravikumar895026 күн бұрын
👍👍
@grengasami92097 ай бұрын
Answer is 1.5
@parimalbose13947 ай бұрын
Dont you think that a very long route has been taken to solve the problem?
@kimngo5197Ай бұрын
3/4
@tanialelaj63272 ай бұрын
=3/2v2
@thomassidoti5496Ай бұрын
its (3*cuberoot(4))/4. What you have is correct but you have to rationalize the denominator. Since we are dealing with cuberoots we have to multiply top and bottom by cuberoot(2) twice (cuberoot(2)*cuberoot(2)*cuberoot(2))=2 and on top you have 3*(cuberoot(2))^2 = (3cuberoot(4)/4)
@kennethwright8708 ай бұрын
Looks like 3/(2✔️2)
@kennethwright8708 ай бұрын
0:33
@terry_willis8 ай бұрын
I made the same mistake. I multiplied by cube root of 2 instead of 4.
@bipmix7 ай бұрын
so you are saying that cube of 4 is 16? not quite
@MrMousley7 ай бұрын
Cube root of 27/16 Cube root of 27 / cube root of 16 3 / cube root of 16 EDIT .. That wasn't it ! 3(cube root of 4) / 4 is simpler ?
@margritkaminsky14708 ай бұрын
3/2 times ÷square rt of 2?
@thomassidoti5496Ай бұрын
If your're trying to write 3/2*cuberoot(2), thats correct but you have to rationalize the denominator. To do that we multiply top and bottom by cuberoot(2)^2. cuberoots must be multiplied out 3 times unlike square roots. So apply that to the denominator, you get 2cuberoot(2) * cuberoot(2)^3 which gives 4 and on top multiply 3*cuberoot(2)^2, we square it here because there was not a cuberoot(2) already there like in the denominator. this gives 3cuberoot(4)/2
@BigAmp7 ай бұрын
Disagree. Acceptable answer is 3/(2*cube root(2)). Reason, Sin 45 is 1/sqrt(2) not sqrt(2)/2. It is acceptable to have radicals in the denominator, well, it was when I was at secondary school 55 years ago.
@aku75987 ай бұрын
3/(2^(1/3) 2)
@stevencraven48974 ай бұрын
3/(2×sqrt
@safiurrahaman44667 ай бұрын
√3×√3=√3²=3,is't?
@Mind_Star902 ай бұрын
If anyone wants to waste their time they can watch this
@tonyjesshope68617 ай бұрын
1.5 all day!
@bobcornwell4038 ай бұрын
I came up with 3/16.
@earnesta.brooks71237 ай бұрын
I think I may have it wrong.
@williambiggs3699Ай бұрын
I'm getting (3*³√2)/4 oops should have multiplied ³√4/³√4 for my "one" used ³√2/³√2 instead (thinking squares instead of cubes. Correct answer is (3*³√4)/4.😂
@mr.mxyzptlks83913 ай бұрын
For this comment, I’ll not even try to solve the question. Just a thought. ‘Many will get wrong’. In all vids. True statement, but it is phrased in the negative, missing an ‘it’ I guess on purpose, some psychology coming in… Personally, not a creator on KZbin , I’d go with ‘Did you get it right?’. Feels much more engaging to me. Just my thoughts, let the shredding begin, as long as it stays within the boundaries of math.
@lieberalsrmarxists832 ай бұрын
I really enjoyed math throughout K-12 and into my graduate studies. I truly enjoy the reviews and the mental exercises. However, your constant talking about things that do not apply to the problem at hand runs my blood pressure up to the point that I cannot listen or watch.
@rocksolid64947 ай бұрын
3/16
@haiyangyu4462Ай бұрын
3 / 2∛2
@srdjannalis30377 ай бұрын
I spent few seconds to solve this simple task you speak ten minutes. Strange scool.
@richardhole84293 ай бұрын
But if you present your short solution to a student, it will not teach them how to arrive at your solution. John is teaching, not just showing the way an advanced level mathematician might do it in his head.
@charlesbusch87397 ай бұрын
You repeat the same things in all your videos. Keep it simple
@RS-Amsterdam3 ай бұрын
Agreed but it is talking to a wall😢
@TomSkinner7 ай бұрын
That's not simplified 😄, different but at least as complicated. Honestly the starting point is cleaner
@nancyfloyd70524 ай бұрын
Sorry 3/2
@rodrodrigues54028 ай бұрын
The claim that Manny will get it wrong is terribly annoying. There is absolutely no need for that.
@suraponwarrarak22397 ай бұрын
Agreed
@sirbrad2336Ай бұрын
He's right. Deal with it.
@edmundhaynes544825 күн бұрын
I agree!
@user-zc6bt4cz6t7 ай бұрын
Сколько лишних слов!
@anngill648120 сағат бұрын
You do waffle on
@berhanegizaw934Күн бұрын
Maths talks much less than this . Please don't bore yuor followers .
@bernardweerasinghe2347 ай бұрын
It might get confused many younger students when you explain too much.
@jimwinchester3397 ай бұрын
How delightful to hear from somebody without an unintelligably thick Indian accent! :P
@wcruzwc628 ай бұрын
Cubic root of 27 = 3 Cubit root of 16 = 2.52 3/2.52 = 1.19
@jamesharmon49948 ай бұрын
The cube root of 16 is not 2.52. The cube root of 16 is irrational.
@janardhanreddy47513 ай бұрын
Waste discussion taking much time
@ECO4738 ай бұрын
Just like in my old s**thole of a high school back in the day...I just didn't get it. WHERE WILL I EVER USE THIS IN NON-STEM WORKING LIFE???
@mathmandrsam8 ай бұрын
It's a great question. Unfortunately, most teachers never explain why we teach certain things. The answer, BTW, to your question is a resounding 'Never'. However, this is not the point. The reason this is taught is because every time your brain is confronted with a challenge it must create new neurological connections in order to find a path to the answer. After a few years of schooling, if you allow this process to take place you will (hopefully) end up with a brain that is better able to seek out solutions.
@louf71788 ай бұрын
It's very basic math. But, yea, don't expect it to be used in basket weaving.
@ECO4738 ай бұрын
@@mathmandrsam Well, that might be. That said, in my professional life, which includes 36 years of tax practice, and 26 years of teaching law, well, cube roots have never come up in any conversation.
@ECO4738 ай бұрын
@@louf7178 Yup!!! Basket Weaving, Tax, Business Law, Finance, Management, Investment Analysis, to name just a few. None of that stuff is relevant to those subject areas, and quite a few more, I would guess.
@terry_willis8 ай бұрын
You will use it when your kids ask for help with their math homework. They will think you're a genius and have more respect for you. :)
@wjgonzalez17 ай бұрын
Too much blather and advertising.
@robertzaleski-ym2du4 ай бұрын
I don't think any student would want to sit and listen to you talk way too much.
@bazsnell31787 ай бұрын
Far too long-winded. Just get on with it already!!
@yessarkae7 ай бұрын
Boring
@user-ux5uy3gs7j7 ай бұрын
Это ещё надо умудриться так бестолково объяснять!! Городить огород полчаса из-за плевого примера!?
@legna68028 ай бұрын
Long explanation ? ? ? Be patient to understand the solution.Don’t be impatient.
@MrSeezero7 ай бұрын
Probably done that way to help keep the advertisements or commercials rolling. If click on certain spots, an advertisement automatically appears.
@frankrawlings4553Ай бұрын
3/2
@charlesbusch87397 ай бұрын
You repeat the same things in all your videos. Keep it simple
@vdharia8 ай бұрын
Answer is 3/4
@kimngo5197Ай бұрын
3/2
@nancyfloyd70524 ай бұрын
3/3
@amnonnesher52537 ай бұрын
3/2
@farjanajahan32226 ай бұрын
3/2
@charlesbusch87397 ай бұрын
You repeat the same things in all your videos. Keep it simple