Simplify Square Root of 63808

Here we will show you two methods that you can use to simplify the square root of 63808. In other words, we will show you how to find the square root of 63808 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.

√63808 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 63808 to simplify the square root of 63808. 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 63808. The factors of 63808 are 1, 2, 4, 8, 16, 32, 64, 997, 1994, 3988, 7976, 15952, 31904, and 63808. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 63808 divided by the greatest perfect square from the list of all factors of 63808. We determined above that the greatest perfect square from the list of all factors of 63808 is 64. Furthermore, 63808 divided by 64 is 997, therefore B equals 997.

Now we have A and B and can get our answer to 63808 in its simplest radical form as follows:

√63808 = A√B

√63808 = 8√997

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 63808 to simplify the square root of 63808 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 63808 and then take the square root of that product. The prime factors that multiply together to make 63808 are 2 x 2 x 2 x 2 x 2 x 2 x 997. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 63808 by the number (A) squared. 8 squared is 64 and 63808 divided by 64 is 997. Therefore, B equals 997.

Once again we have A and B and can get our answer to 63808 in its simplest radical form as follows:

√63808 = A√B

√63808 = 8√997

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Simplify Square Root of 63809
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