Simplify Square Root of 23148

Here we will show you two methods that you can use to simplify the square root of 23148. In other words, we will show you how to find the square root of 23148 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.

√23148 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 23148 to simplify the square root of 23148. 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 23148. The factors of 23148 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 643, 1286, 1929, 2572, 3858, 5787, 7716, 11574, and 23148. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 23148 divided by the greatest perfect square from the list of all factors of 23148. We determined above that the greatest perfect square from the list of all factors of 23148 is 36. Furthermore, 23148 divided by 36 is 643, therefore B equals 643.

Now we have A and B and can get our answer to 23148 in its simplest radical form as follows:

√23148 = A√B

√23148 = 6√643

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 23148 to simplify the square root of 23148 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 23148 and then take the square root of that product. The prime factors that multiply together to make 23148 are 2 x 2 x 3 x 3 x 643. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 23148 by the number (A) squared. 6 squared is 36 and 23148 divided by 36 is 643. Therefore, B equals 643.

Once again we have A and B and can get our answer to 23148 in its simplest radical form as follows:

√23148 = A√B

√23148 = 6√643

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Simplify Square Root of 23149
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