Simplify Square Root of 97216

Here we will show you two methods that you can use to simplify the square root of 97216. In other words, we will show you how to find the square root of 97216 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.

√97216 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 97216 to simplify the square root of 97216. 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 97216. The factors of 97216 are 1, 2, 4, 7, 8, 14, 16, 28, 31, 32, 49, 56, 62, 64, 98, 112, 124, 196, 217, 224, 248, 392, 434, 448, 496, 784, 868, 992, 1519, 1568, 1736, 1984, 3038, 3136, 3472, 6076, 6944, 12152, 13888, 24304, 48608, and 97216. Furthermore, the greatest perfect square on this list is 3136 and the square root of 3136 is 56. Therefore, A equals 56.

B = Calculate 97216 divided by the greatest perfect square from the list of all factors of 97216. We determined above that the greatest perfect square from the list of all factors of 97216 is 3136. Furthermore, 97216 divided by 3136 is 31, therefore B equals 31.

Now we have A and B and can get our answer to 97216 in its simplest radical form as follows:

√97216 = A√B

√97216 = 56√31

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 97216 to simplify the square root of 97216 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 97216 and then take the square root of that product. The prime factors that multiply together to make 97216 are 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7 x 31. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7 = 3136 and the square root of 3136 is 56. Therefore, A equals 56.

B = Divide 97216 by the number (A) squared. 56 squared is 3136 and 97216 divided by 3136 is 31. Therefore, B equals 31.

Once again we have A and B and can get our answer to 97216 in its simplest radical form as follows:

√97216 = A√B

√97216 = 56√31

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