Lesson: Properties of Roots

Comment on Properties of Roots

Abdul Hannan's picture

Hello Mr Hanneson, is there any way to calculate nth root of any number on the GRE Calculator. I know a trick on the simple calculator, but it doesn't work on the GRE calculator.
thankyou
greenlight-admin's picture

Great question!

There are a few roots that are easy to calculate.

For example, if want want to calculate the 4th root of 81, we can first find the square root of 81, and then find the square root of the result.
Here's why this works:
The fourth root of x = x^(1/4)
The square root of x = x^(1/2)
Now notice that [x^(1/2)]^(1/2) = x^(1/4)...voila!

We can also use a similar strategy to find the 8th root of x
To calculate the 8th root of x, first find the square root of x, and then press the square root button a second time, and then press the square root button a third time
Here's why it works:
The eighth root of x = x^(1/8)
Now notice that [[x^(1/2)]^(1/2)]^(1/2) = x^(1/8)...tada!!!

For reference, here's the link to the lesson covering the GRE: https://www.greenlighttestprep.com/module/general-gre-info-and-strategie...

Cheers,
Brent

Hi,
in the following question answer is D
https://greprepclub.com/forum/if-x-0-then-must-be-equal-to-0-07x8-0-07x4-0-7x14-0-7x8-11477.html

the result is correct but it says A instead of D.
greenlight-admin's picture

Good catch!
I've edited my response.

Cheers and thanks!
Brent

Hey brent.

Since √x = x^1/2, can I say that √x^4 = x^(4/2) = x^2 ?
greenlight-admin's picture

Sorry for the delay. I'm not sure how I missed this question.

Yes, if x ≥ 0, we can say that (√x)^4 = √(x^4) = x^(4/2) = x^2

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