Simplify Square Root of 13952

Here we will show you two methods that you can use to simplify the square root of 13952. In other words, we will show you how to find the square root of 13952 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.

√13952 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 13952 to simplify the square root of 13952. 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 13952. The factors of 13952 are 1, 2, 4, 8, 16, 32, 64, 109, 128, 218, 436, 872, 1744, 3488, 6976, and 13952. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 13952 divided by the greatest perfect square from the list of all factors of 13952. We determined above that the greatest perfect square from the list of all factors of 13952 is 64. Furthermore, 13952 divided by 64 is 218, therefore B equals 218.

Now we have A and B and can get our answer to 13952 in its simplest radical form as follows:

√13952 = A√B

√13952 = 8√218

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 13952 to simplify the square root of 13952 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 13952 and then take the square root of that product. The prime factors that multiply together to make 13952 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 109. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 13952 by the number (A) squared. 8 squared is 64 and 13952 divided by 64 is 218. Therefore, B equals 218.

Once again we have A and B and can get our answer to 13952 in its simplest radical form as follows:

√13952 = A√B

√13952 = 8√218

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Simplify Square Root of 13953
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