How to find the square root of a square root?

In summary, the conversation is about simplifying the expression √(53 - 8√15) using the equation √a - √b. The person attempted to make an equation where the two expressions were equal and also tried to use perfect squares, but was unsure how to proceed. Eventually, with the help of another person, they were able to solve the problem and get the answer 4√3 - √5.
  • #1
Cheesycheese213
55
8

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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  • #2
Cheesycheese213 said:

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}\,? ##
 
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  • #3
SammyS said:
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
Cheesycheese213 said:
Ohhhh I see! Thank you so much!
So, did you solve the problem? If so what is your answer?
 
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  • #5
I got 4√3 - √5! Thanks again! :smile::smile::smile:
 
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1. What is a square root of a square root?

A square root of a square root is the number that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, and the square root of 3 is approximately 1.732.

2. Why would I need to find the square root of a square root?

Finding the square root of a square root is often necessary in advanced mathematical equations and calculations. It can also be used to simplify complex expressions and solve certain problems.

3. How do I find the square root of a square root?

To find the square root of a square root, you can use the power rule for radicals. This rule states that the square root of a number raised to a power is equal to the number raised to half of that power. For example, the square root of the square root of 16 is equal to 16^(1/4), which is 2.

4. Can I use a calculator to find the square root of a square root?

Yes, most calculators have a square root function that can be used to find the square root of a square root. Simply enter the number, press the square root button, and then press the equal sign. Some calculators may also have a power function that can be used to find the square root of a square root.

5. Are there any special considerations when finding the square root of a square root?

Yes, it is important to pay attention to the order of operations when finding the square root of a square root. Make sure to take the square root of the number inside the parentheses first, and then take the square root of the resulting number. It is also important to note that the square root of a negative number is not a real number, so it is not possible to find the square root of a square root of a negative number.

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