# How to find the square root of a square root?

## Homework Statement

Simplify √(53 - 8√15)

## Homework Equations

Numbers can be represented as √a - √b

## The Attempt at a Solution

I had tried to make in an equation where the 2 expressions were equal, but after squaring both sides, I didn’t really know what to do.
I had also tried to use something like making a perfect square, and I did get a number, though it was much longer and more complicated, and I don’t think that’s right.
Now I’m a bit lost, and I’m not sure how to use the √a - √b that the teacher gave us.
Thanks!!

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SammyS
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Homework Helper
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## Homework Statement

Simplify √(53 - 8√15)

## Homework Equations

Numbers can be represented as √a - √b

## The Attempt at a Solution

I had tried to make in an equation where the 2 expressions were equal, but after squaring both sides, I didn’t really know what to do.
I had also tried to use something like making a perfect square, and I did get a number, though it was much longer and more complicated, and I don’t think that’s right.
Now I’m a bit lost, and I’m not sure how to use the √a - √b that the teacher gave us.
Thanks!!
What did you get when you squared both sides? In particular, what did you get when you squared $\ \sqrt{a}-\sqrt{b}\,?$

What did you get when you squared both sides? In particular, what did you get when you squared $\ \sqrt{a}-\sqrt{b}\,?$
Ohhhh I see!!! Thank you so much!!!!

SammyS
Staff Emeritus
Homework Helper
Gold Member
Ohhhh I see!!! Thank you so much!!!!
So, did you solve the problem? If so what is your answer?

• YoungPhysicist
I got 4√3 - √5! Thanks again!!   • YoungPhysicist