Lesson: Other Roots

Comment on Other Roots

You say a root will have at most 1 value. But doesn't the 4th root of 16 = 2 and -2, because 2^4 = 16 and -2^4 = 16? Thanks!
gmat-admin's picture

When it comes to root notation involving even roots (e.g.m square root, 4th root, 6th root, 8th root, etc.), the root NOTATION tells us to take only the positive root.

So on the gmat test, will is also follow this rule ?
gmat-admin's picture

Yes, most definitely.

Reinforcement activities (counting top-down) #1 and #5 link to the same exercise.
gmat-admin's picture

Thanks for the heads up, BalysLTU!
I have removed one of the links.


Hi Brent,

Could you solve this qs - https://gmatclub.com/forum/if-k-is-a-positive-integer-is-k-a-prime-number-96118.html

Why is even root of a positive number always positive?

Isn't (-5)^4 also 625?
gmat-admin's picture

Great question!!

Consider √9
There are two values that, when squared, result in 9.
Those two values are 3 and -3.
As you can imagine, it would be confusing for √9 to have more than one value.
For example, if I told you that x = √25, you wouldn't know whether x = 5 or x = -5.

So, mathematicians came up with the following construct:
√k = the POSITIVE value that, when squared, equals k, and -√k = the NEGATIVE value that, when squared, equals k.
That way, we can represent the positive square root one way, I represent the negative square root another (different) way

So, it all comes down to NOTATION.
We'll use √k to represent the POSITIVE square root of k, and we'll use -√k to represent the NEGATIVE square root of k.

Some examples:
√49 = 7
-√81 = -9
-√100 = -10
√16 = 4

This construct applies to all even roots.
For example, ∜16 = 2, and -∜16 = -2
Likewise, ∜625 = 5, and -∜625 = -5

Does that help?

In this question - https://gmatclub.com/forum/if-a-and-b-are-positive-integers-is-ab-an-an-integer-223747.html

In statement 2, if b = 2, a = 4, statement becomes insufficient.
Can you please explain?
gmat-admin's picture

Question link: https://gmatclub.com/forum/if-a-and-b-are-positive-integers-is-ab-an-an-...

I'm not sure what you mean when you say " statement becomes insufficient"

We can never conclude that a statement is not sufficient by testing only ONE value.

You are correct to say that the pair of values, b = 2 & a = 4, satisfy statement 2, and when we plug those values into the target question (Is the cuberoot of ab an integer?) the answer to the target question is: YES, the cuberoot of ab an integer IS an integer.

To show that statement 2 is insufficient, you must now find a second pair of values that satisfy statement 2, but yield a different answer to the target question (i.e., NO, the cuberoot of ab an integer is NOT an integer.

For more on testing values in a data sufficiency question, you might want to watch the following video: https://www.gmatprepnow.com/module/gmat-data-sufficiency/video/1101

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