Simplify Square Root of 27508

Here we will show you two methods that you can use to simplify the square root of 27508. In other words, we will show you how to find the square root of 27508 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.

√27508 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 27508 to simplify the square root of 27508. 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 27508. The factors of 27508 are 1, 2, 4, 13, 23, 26, 46, 52, 92, 299, 529, 598, 1058, 1196, 2116, 6877, 13754, and 27508. Furthermore, the greatest perfect square on this list is 2116 and the square root of 2116 is 46. Therefore, A equals 46.

B = Calculate 27508 divided by the greatest perfect square from the list of all factors of 27508. We determined above that the greatest perfect square from the list of all factors of 27508 is 2116. Furthermore, 27508 divided by 2116 is 13, therefore B equals 13.

Now we have A and B and can get our answer to 27508 in its simplest radical form as follows:

√27508 = A√B

√27508 = 46√13

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 27508 to simplify the square root of 27508 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 27508 and then take the square root of that product. The prime factors that multiply together to make 27508 are 2 x 2 x 13 x 23 x 23. When we strip out the pairs only, we get 2 x 2 x 23 x 23 = 2116 and the square root of 2116 is 46. Therefore, A equals 46.

B = Divide 27508 by the number (A) squared. 46 squared is 2116 and 27508 divided by 2116 is 13. Therefore, B equals 13.

Once again we have A and B and can get our answer to 27508 in its simplest radical form as follows:

√27508 = A√B

√27508 = 46√13

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Simplify Square Root of 27509
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