Simplify Square Root of 2527

Here we will show you two methods that you can use to simplify the square root of 2527. In other words, we will show you how to find the square root of 2527 in its simplest radical form using two different methods.

To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√2527 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 2527 to simplify the square root of 2527. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 2527. The factors of 2527 are 1, 7, 19, 133, 361, and 2527. Furthermore, the greatest perfect square on this list is 361 and the square root of 361 is 19. Therefore, A equals 19.

B = Calculate 2527 divided by the greatest perfect square from the list of all factors of 2527. We determined above that the greatest perfect square from the list of all factors of 2527 is 361. Furthermore, 2527 divided by 361 is 7, therefore B equals 7.

Now we have A and B and can get our answer to 2527 in its simplest radical form as follows:

√2527 = A√B

√2527 = 19√7

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 2527 to simplify the square root of 2527 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 2527 and then take the square root of that product. The prime factors that multiply together to make 2527 are 7 x 19 x 19. When we strip out the pairs only, we get 19 x 19 = 361 and the square root of 361 is 19. Therefore, A equals 19.

B = Divide 2527 by the number (A) squared. 19 squared is 361 and 2527 divided by 361 is 7. Therefore, B equals 7.

Once again we have A and B and can get our answer to 2527 in its simplest radical form as follows:

√2527 = A√B

√2527 = 19√7

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Simplify Square Root of 2528
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