Simplify the Cube Root Radical Expression. MOST will NOT Get RIGHT!
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- เผยแพร่เมื่อ 2 มิ.ย. 2024
- Simplify a cube root radical expression.
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It has been over 40 years since I encountered that sort of problem Thanks for the refresher.
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!❤
Thank you so much. Another excellent video! So correct about textbooks not teaching this!
great one. only missed the final factor. always fun though. thanks.
I prefer the result 3/(2*cuberoot (2))
That's exactly what it should be
yep me too 16=8*2 yeilding 2*cuberoot(2)
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).
That is rounded 1.19.
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.
That's where I made my mistake.
3/4 (cube root of 4)
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.
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
Cube root of 4/64!!
I never would have thought of that. Great stuff! Thanks.
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.
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
i wonder how many of his students fall asleep from boredom because he takes forever to get to the solution to the problem.
What are your thoughts on (3 x 2^(2/3)) / 4?
My thoughts precisely too
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.
Many will get this wrong! How many? You must have really blessed students.
I'm astonished at the number of people watching his very basic videos. I do it as a research for viewing statistics myself.
Thankyou sir ! denominator rules 🙏
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.
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!
Thank' !
Did this in my head.
3/2 x (Cube Root of 1/2)
Yes, but rationalize the denominator.
@@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.
@@silverhammer7779 That bridge will not stand very long with a rational in the denominator.
Why didn't you divide the square root 4 to get 2. Thanks answer
Takes me back to my highschool days.
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. 🤔
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. 😊
(3cubed root of 4)/4
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
16 is 2 cubed x 2. 8 is the cube of 2.
Explanation is too much
I got the answer in about 10 seconds.
Dozed off in the middle bit. Knew the answer anyway.
It is far better to explain too much than too little.
That’s the point of the channel.
@@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.
Cubic of 2×3/2
This problem is easier if you use fractional exponents and rationalize the denominator.
3/2 times ÷square rt of 2?
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.
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.
I came up with 3/16.
1.5
1.5 all day!
Dont you think that a very long route has been taken to solve the problem?
Looks like
3/(2✔️2)
0:33
I made the same mistake. I multiplied by cube root of 2 instead of 4.
3/(2^(1/3) 2)
What's wrong with 3/2 × ∛(1/2)?
That will be too easy for him and not enough time wasting!
3/3
3/2
so you are saying that cube of 4 is 16? not quite
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 ?
Answer is 1.5
3/(2×sqrt
3/16
I think I may have it wrong.
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.
√3×√3=√3²=3,is't?
I spent few seconds to solve this simple task you speak ten minutes. Strange scool.
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.
That's not simplified 😄, different but at least as complicated. Honestly the starting point is cleaner
Sorry 3/2
The claim that Manny will get it wrong is terribly annoying. There is absolutely no need for that.
Agreed
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???
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.
It's very basic math. But, yea, don't expect it to be used in basket weaving.
@@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.
@@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.
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. :)
Answer is 3/4
Сколько лишних слов!
It might get confused many younger students when you explain too much.
You repeat the same things in all your videos. Keep it simple
How delightful to hear from somebody without an unintelligably thick Indian accent! :P
Waste discussion taking much time
I don't think any student would want to sit and listen to you talk way too much.
Far too long-winded. Just get on with it already!!
Too much blather and advertising.
Cubic root of 27 = 3
Cubit root of 16 = 2.52
3/2.52 = 1.19
The cube root of 16 is not 2.52. The cube root of 16 is irrational.
Boring
Это ещё надо умудриться так бестолково объяснять!! Городить огород полчаса из-за плевого примера!?
Long explanation ? ? ? Be patient to understand the solution.Don’t be impatient.
Probably done that way to help keep the advertisements or commercials rolling. If click on certain spots, an advertisement automatically appears.
3/2
You repeat the same things in all your videos. Keep it simple
You repeat the same things in all your videos. Keep it simple