Simplify Square Root of 97167

Here we will show you two methods that you can use to simplify the square root of 97167. In other words, we will show you how to find the square root of 97167 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.

√97167 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 97167 to simplify the square root of 97167. 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 97167. The factors of 97167 are 1, 3, 7, 21, 49, 147, 661, 1983, 4627, 13881, 32389, and 97167. Furthermore, the greatest perfect square on this list is 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Calculate 97167 divided by the greatest perfect square from the list of all factors of 97167. We determined above that the greatest perfect square from the list of all factors of 97167 is 49. Furthermore, 97167 divided by 49 is 1983, therefore B equals 1983.

Now we have A and B and can get our answer to 97167 in its simplest radical form as follows:

√97167 = A√B

√97167 = 7√1983

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 97167 to simplify the square root of 97167 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 97167 and then take the square root of that product. The prime factors that multiply together to make 97167 are 3 x 7 x 7 x 661. When we strip out the pairs only, we get 7 x 7 = 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Divide 97167 by the number (A) squared. 7 squared is 49 and 97167 divided by 49 is 1983. Therefore, B equals 1983.

Once again we have A and B and can get our answer to 97167 in its simplest radical form as follows:

√97167 = A√B

√97167 = 7√1983

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Simplify Square Root of 97168
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