How to find the square root of a square root?

[Cheesycheese213]

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!

 

[SammyS]

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 $\ \sqrt{a}-\sqrt{b}\,?$

 

[Cheesycheese213]

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]

Ohhhh I see! Thank you so much!

So, did you solve the problem? If so what is your answer?

 

[Cheesycheese213]

I got 4√3 - √5! Thanks again!