Simplify Square Root of 95139

Here we will show you two methods that you can use to simplify the square root of 95139. In other words, we will show you how to find the square root of 95139 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.

√95139 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 95139 to simplify the square root of 95139. 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 95139. The factors of 95139 are 1, 3, 9, 11, 31, 33, 93, 99, 279, 341, 961, 1023, 2883, 3069, 8649, 10571, 31713, and 95139. Furthermore, the greatest perfect square on this list is 8649 and the square root of 8649 is 93. Therefore, A equals 93.

B = Calculate 95139 divided by the greatest perfect square from the list of all factors of 95139. We determined above that the greatest perfect square from the list of all factors of 95139 is 8649. Furthermore, 95139 divided by 8649 is 11, therefore B equals 11.

Now we have A and B and can get our answer to 95139 in its simplest radical form as follows:

√95139 = A√B

√95139 = 93√11

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 95139 to simplify the square root of 95139 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 95139 and then take the square root of that product. The prime factors that multiply together to make 95139 are 3 x 3 x 11 x 31 x 31. When we strip out the pairs only, we get 3 x 3 x 31 x 31 = 8649 and the square root of 8649 is 93. Therefore, A equals 93.

B = Divide 95139 by the number (A) squared. 93 squared is 8649 and 95139 divided by 8649 is 11. Therefore, B equals 11.

Once again we have A and B and can get our answer to 95139 in its simplest radical form as follows:

√95139 = A√B

√95139 = 93√11

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Simplify Square Root of 95140
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