Simplify Square Root of 96575

Here we will show you two methods that you can use to simplify the square root of 96575. In other words, we will show you how to find the square root of 96575 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.

√96575 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 96575 to simplify the square root of 96575. 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 96575. The factors of 96575 are 1, 5, 25, 3863, 19315, and 96575. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 96575 divided by the greatest perfect square from the list of all factors of 96575. We determined above that the greatest perfect square from the list of all factors of 96575 is 25. Furthermore, 96575 divided by 25 is 3863, therefore B equals 3863.

Now we have A and B and can get our answer to 96575 in its simplest radical form as follows:

√96575 = A√B

√96575 = 5√3863

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 96575 to simplify the square root of 96575 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 96575 and then take the square root of that product. The prime factors that multiply together to make 96575 are 5 x 5 x 3863. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 96575 by the number (A) squared. 5 squared is 25 and 96575 divided by 25 is 3863. Therefore, B equals 3863.

Once again we have A and B and can get our answer to 96575 in its simplest radical form as follows:

√96575 = A√B

√96575 = 5√3863

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Simplify Square Root of 96576
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