# Quantitative Question

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What is this ^

I thought it was the square root of 87 times 3?

If x and y are the integers most nearly equal to  and x <  < y, what is the value of xy

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That is a cubic root.
A simpler example would be 2 is the cubic root of 8 (23 = 8)

Thus, find the cube root of 87 and go from there

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I am not sure if you have the "cubic root" function on the GRE on-screen calculator. It might help to know that 87 to the power of (1/3) is the same as a cubic root (and things to the power of 1/2 is the same as a square root, etc.)

However, a good tip for these types of question is to not actually solve for the cubic root of 87 but to find the closest "easy" cubic roots. 4x4x4 = 64 and 5x5x5 = 125, so you know that the cubic root of 87, is between 4 and 5 because 87 is between 64 and 125. The exact value of the cubic root of 87 does not really matter, you just need to know it's close to 4 and 5

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I am not sure if you have the "cubic root" function on the GRE on-screen calculator. It might help to know that 87 to the power of (1/3) is the same as a cubic root (and things to the power of 1/2 is the same as a square root, etc.)

However, a good tip for these types of question is to not actually solve for the cubic root of 87 but to find the closest "easy" cubic roots. 4x4x4 = 64 and 5x5x5 = 125, so you know that the cubic root of 87, is between 4 and 5 because 87 is between 64 and 125. The exact value of the cubic root of 87 does not really matter, you just need to know it's close to 4 and 5

Perfect. That makes sense. Where in life I will have to apply this is beyond me, but if I have to know cubic roots for the GRE so be it! It's been about 8 years since I've done this type of math, so need to touch up on basic concepts.

Edited by westy3789
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Perfect. That makes sense. Where in life I will have to apply this is beyond me, but if I have to know cubic roots for the GRE so be it! It's been about 8 years since I've done this type of math, so need to touch up on basic concepts.

I don't mean to defend standardized test questions but I just can't help but defend "math" when its applications are questioned Sorry, but here goes:

Cubic roots (or basically, just the concept of inverting the "something times itself 3 times") is useful to estimate volumes, since volumes are something like Length x Width x Height. So if you have a container that you're told is 1000 cubic feet, you might not be able to visualize that easily. But if you know the cube root of 1000 is 10 (since 10x10x10 = 1000) then you know that 1000 cubic feet is a cube that is 10 feet on each side.

Also, for this GRE question, you are not really being tested on what a cubic root is. I think the real skill being tested is the "in between estimation" logic I wrote above. Cubic roots are just something complex enough that you can't just figure out the cubic root of 87 in your head, and therefore must find two answers that you do know (cubic root of 64=4 and cubic root of 125=5) in order to estimate that the real answer is between 4 and 5. Guessing the answer to a complex problem by placing in between 2 previously known (or easier to find) answers is a useful skill in both life and quantitative research!

Okay, rant over, sorry for any inconvenience!

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I don't mean to defend standardized test questions but I just can't help but defend "math" when its applications are questioned Sorry, but here goes:

Cubic roots (or basically, just the concept of inverting the "something times itself 3 times") is useful to estimate volumes, since volumes are something like Length x Width x Height. So if you have a container that you're told is 1000 cubic feet, you might not be able to visualize that easily. But if you know the cube root of 1000 is 10 (since 10x10x10 = 1000) then you know that 1000 cubic feet is a cube that is 10 feet on each side.

Also, for this GRE question, you are not really being tested on what a cubic root is. I think the real skill being tested is the "in between estimation" logic I wrote above. Cubic roots are just something complex enough that you can't just figure out the cubic root of 87 in your head, and therefore must find two answers that you do know (cubic root of 64=4 and cubic root of 125=5) in order to estimate that the real answer is between 4 and 5. Guessing the answer to a complex problem by placing in between 2 previously known (or easier to find) answers is a useful skill in both life and quantitative research!

Okay, rant over, sorry for any inconvenience!

Okay, well...for the average person, like myself, I don't use cubic roots to estimate volumes ha. I have never estimated a volume using a cubic root once in my life outside a math course. But I agree that there's an application for it..I also agree that it's testing "in between estimation" logic vs. cubic root theory, which is more pragmatic.

Although however impractical the application is, i must admit it's requiring the use of a certain thought process that implies a person's ability to think logically.

Edited by westy3789

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