Simplify Square Root of 65863

Here we will show you two methods that you can use to simplify the square root of 65863. In other words, we will show you how to find the square root of 65863 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.

√65863 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 65863 to simplify the square root of 65863. 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 65863. The factors of 65863 are 1, 7, 97, 679, 9409, and 65863. Furthermore, the greatest perfect square on this list is 9409 and the square root of 9409 is 97. Therefore, A equals 97.

B = Calculate 65863 divided by the greatest perfect square from the list of all factors of 65863. We determined above that the greatest perfect square from the list of all factors of 65863 is 9409. Furthermore, 65863 divided by 9409 is 7, therefore B equals 7.

Now we have A and B and can get our answer to 65863 in its simplest radical form as follows:

√65863 = A√B

√65863 = 97√7

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 65863 to simplify the square root of 65863 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 65863 and then take the square root of that product. The prime factors that multiply together to make 65863 are 7 x 97 x 97. When we strip out the pairs only, we get 97 x 97 = 9409 and the square root of 9409 is 97. Therefore, A equals 97.

B = Divide 65863 by the number (A) squared. 97 squared is 9409 and 65863 divided by 9409 is 7. Therefore, B equals 7.

Once again we have A and B and can get our answer to 65863 in its simplest radical form as follows:

√65863 = A√B

√65863 = 97√7

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Simplify Square Root of 65864
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