Simplify Square Root of 95697

Here we will show you two methods that you can use to simplify the square root of 95697. In other words, we will show you how to find the square root of 95697 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.

√95697 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 95697 to simplify the square root of 95697. 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 95697. The factors of 95697 are 1, 3, 7, 9, 21, 31, 49, 63, 93, 147, 217, 279, 343, 441, 651, 1029, 1519, 1953, 3087, 4557, 10633, 13671, 31899, and 95697. Furthermore, the greatest perfect square on this list is 441 and the square root of 441 is 21. Therefore, A equals 21.

B = Calculate 95697 divided by the greatest perfect square from the list of all factors of 95697. We determined above that the greatest perfect square from the list of all factors of 95697 is 441. Furthermore, 95697 divided by 441 is 217, therefore B equals 217.

Now we have A and B and can get our answer to 95697 in its simplest radical form as follows:

√95697 = A√B

√95697 = 21√217

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 95697 to simplify the square root of 95697 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 95697 and then take the square root of that product. The prime factors that multiply together to make 95697 are 3 x 3 x 7 x 7 x 7 x 31. When we strip out the pairs only, we get 3 x 3 x 7 x 7 = 441 and the square root of 441 is 21. Therefore, A equals 21.

B = Divide 95697 by the number (A) squared. 21 squared is 441 and 95697 divided by 441 is 217. Therefore, B equals 217.

Once again we have A and B and can get our answer to 95697 in its simplest radical form as follows:

√95697 = A√B

√95697 = 21√217

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Simplify Square Root of 95698
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