Simplify Square Root of 97952

Here we will show you two methods that you can use to simplify the square root of 97952. In other words, we will show you how to find the square root of 97952 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.

√97952 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 97952 to simplify the square root of 97952. 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 97952. The factors of 97952 are 1, 2, 4, 8, 16, 32, 3061, 6122, 12244, 24488, 48976, and 97952. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 97952 divided by the greatest perfect square from the list of all factors of 97952. We determined above that the greatest perfect square from the list of all factors of 97952 is 16. Furthermore, 97952 divided by 16 is 6122, therefore B equals 6122.

Now we have A and B and can get our answer to 97952 in its simplest radical form as follows:

√97952 = A√B

√97952 = 4√6122

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 97952 to simplify the square root of 97952 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 97952 and then take the square root of that product. The prime factors that multiply together to make 97952 are 2 x 2 x 2 x 2 x 2 x 3061. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 97952 by the number (A) squared. 4 squared is 16 and 97952 divided by 16 is 6122. Therefore, B equals 6122.

Once again we have A and B and can get our answer to 97952 in its simplest radical form as follows:

√97952 = A√B

√97952 = 4√6122

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Simplify Square Root of 97953
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