Simplify Square Root of 23548

Here we will show you two methods that you can use to simplify the square root of 23548. In other words, we will show you how to find the square root of 23548 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.

√23548 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 23548 to simplify the square root of 23548. 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 23548. The factors of 23548 are 1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812, 841, 1682, 3364, 5887, 11774, and 23548. Furthermore, the greatest perfect square on this list is 3364 and the square root of 3364 is 58. Therefore, A equals 58.

B = Calculate 23548 divided by the greatest perfect square from the list of all factors of 23548. We determined above that the greatest perfect square from the list of all factors of 23548 is 3364. Furthermore, 23548 divided by 3364 is 7, therefore B equals 7.

Now we have A and B and can get our answer to 23548 in its simplest radical form as follows:

√23548 = A√B

√23548 = 58√7

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 23548 to simplify the square root of 23548 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 23548 and then take the square root of that product. The prime factors that multiply together to make 23548 are 2 x 2 x 7 x 29 x 29. When we strip out the pairs only, we get 2 x 2 x 29 x 29 = 3364 and the square root of 3364 is 58. Therefore, A equals 58.

B = Divide 23548 by the number (A) squared. 58 squared is 3364 and 23548 divided by 3364 is 7. Therefore, B equals 7.

Once again we have A and B and can get our answer to 23548 in its simplest radical form as follows:

√23548 = A√B

√23548 = 58√7

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Simplify Square Root of 23549
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