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
gmat-admin's picture

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?

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