# Thread: square root of a square root

1. ## square root of a square root

Hi,

If x & y are both positive:

$\sqrt{8\sqrt{4x^8y^{10}}}$= ?

I am not sure how to do this problem. Thanks!

2. Originally Posted by cottongirl
Hi,

If x & y are both positive:

$\sqrt{8\sqrt{4x^8y^{10}}}$= ?

I am not sure how to do this problem. Thanks!
Hi cottongirl,

You can simplify the nested square root first since everything under that radical is a perfect square:

$\sqrt{8\sqrt{4x^8y^{10}}} = \sqrt{8 \cdot2x^4y^5}$

You should be able to finish up now, right?

3. Thank you !!! Ok, so taking the square root of a number with an exponent, you don't take the square root of the exponent, you just divide it by 2?

4. Originally Posted by cottongirl
Thank you !!! Ok, so taking the square root of a number with an exponent, you don't take the square root of the exponent, you just divide it by 2?
Hi cottongirl,

That is true for the square root. If the exponent is even, that's good. If the exponent is odd, then you'll always have a remainder of 1. For instance,

$\sqrt{y^5}=\sqrt{y^4 \cdot y^1}=y^2\sqrt{y}$

5. Originally Posted by cottongirl
Thank you !!! Ok, so taking the square root of a number with an exponent, you don't take the square root of the exponent, you just divide it by 2?
Radicals can be converted to fractional exponents. For a square root, the power is one-half; for a cube root, the power is one-third; and so forth.

6. Is this right?

$4x^2 y^2 \sqrt{y}$

7. Originally Posted by cottongirl
Is this right?

$4x^2 y^2 \sqrt{y}$
You are correct!