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How to find the square root of a square root?

  • #1

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!!
 

Answers and Replies

  • #2
SammyS
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Science Advisor
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}\,? ##
 
  • #3
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!!!!
 
  • #4
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,254
972
Ohhhh I see!!! Thank you so much!!!!
So, did you solve the problem? If so what is your answer?
 
  • #5
I got 4√3 - √5! Thanks again!! :smile::smile::smile:
 

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