Simplify Square Root of 23175

Here we will show you two methods that you can use to simplify the square root of 23175. In other words, we will show you how to find the square root of 23175 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.

√23175 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 23175 to simplify the square root of 23175. 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 23175. The factors of 23175 are 1, 3, 5, 9, 15, 25, 45, 75, 103, 225, 309, 515, 927, 1545, 2575, 4635, 7725, and 23175. Furthermore, the greatest perfect square on this list is 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Calculate 23175 divided by the greatest perfect square from the list of all factors of 23175. We determined above that the greatest perfect square from the list of all factors of 23175 is 225. Furthermore, 23175 divided by 225 is 103, therefore B equals 103.

Now we have A and B and can get our answer to 23175 in its simplest radical form as follows:

√23175 = A√B

√23175 = 15√103

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 23175 to simplify the square root of 23175 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 23175 and then take the square root of that product. The prime factors that multiply together to make 23175 are 3 x 3 x 5 x 5 x 103. When we strip out the pairs only, we get 3 x 3 x 5 x 5 = 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Divide 23175 by the number (A) squared. 15 squared is 225 and 23175 divided by 225 is 103. Therefore, B equals 103.

Once again we have A and B and can get our answer to 23175 in its simplest radical form as follows:

√23175 = A√B

√23175 = 15√103

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Simplify Square Root of 23176
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