Simplify Square Root of 23491

Here we will show you two methods that you can use to simplify the square root of 23491. In other words, we will show you how to find the square root of 23491 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.

√23491 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 23491 to simplify the square root of 23491. 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 23491. The factors of 23491 are 1, 13, 139, 169, 1807, and 23491. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 23491 divided by the greatest perfect square from the list of all factors of 23491. We determined above that the greatest perfect square from the list of all factors of 23491 is 169. Furthermore, 23491 divided by 169 is 139, therefore B equals 139.

Now we have A and B and can get our answer to 23491 in its simplest radical form as follows:

√23491 = A√B

√23491 = 13√139

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 23491 to simplify the square root of 23491 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 23491 and then take the square root of that product. The prime factors that multiply together to make 23491 are 13 x 13 x 139. When we strip out the pairs only, we get 13 x 13 = 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Divide 23491 by the number (A) squared. 13 squared is 169 and 23491 divided by 169 is 139. Therefore, B equals 139.

Once again we have A and B and can get our answer to 23491 in its simplest radical form as follows:

√23491 = A√B

√23491 = 13√139

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Simplify Square Root of 23492
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