Simplify Square Root of 13122

Here we will show you two methods that you can use to simplify the square root of 13122. In other words, we will show you how to find the square root of 13122 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.

√13122 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 13122 to simplify the square root of 13122. 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 13122. The factors of 13122 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486, 729, 1458, 2187, 4374, 6561, and 13122. Furthermore, the greatest perfect square on this list is 6561 and the square root of 6561 is 81. Therefore, A equals 81.

B = Calculate 13122 divided by the greatest perfect square from the list of all factors of 13122. We determined above that the greatest perfect square from the list of all factors of 13122 is 6561. Furthermore, 13122 divided by 6561 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 13122 in its simplest radical form as follows:

√13122 = A√B

√13122 = 81√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 13122 to simplify the square root of 13122 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 13122 and then take the square root of that product. The prime factors that multiply together to make 13122 are 2 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 = 6561 and the square root of 6561 is 81. Therefore, A equals 81.

B = Divide 13122 by the number (A) squared. 81 squared is 6561 and 13122 divided by 6561 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 13122 in its simplest radical form as follows:

√13122 = A√B

√13122 = 81√2

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Simplify Square Root of 13123
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