Simplify Square Root of 63568

Here we will show you two methods that you can use to simplify the square root of 63568. In other words, we will show you how to find the square root of 63568 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.

√63568 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 63568 to simplify the square root of 63568. 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 63568. The factors of 63568 are 1, 2, 4, 8, 16, 29, 58, 116, 137, 232, 274, 464, 548, 1096, 2192, 3973, 7946, 15892, 31784, and 63568. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 63568 divided by the greatest perfect square from the list of all factors of 63568. We determined above that the greatest perfect square from the list of all factors of 63568 is 16. Furthermore, 63568 divided by 16 is 3973, therefore B equals 3973.

Now we have A and B and can get our answer to 63568 in its simplest radical form as follows:

√63568 = A√B

√63568 = 4√3973

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 63568 to simplify the square root of 63568 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 63568 and then take the square root of that product. The prime factors that multiply together to make 63568 are 2 x 2 x 2 x 2 x 29 x 137. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 63568 by the number (A) squared. 4 squared is 16 and 63568 divided by 16 is 3973. Therefore, B equals 3973.

Once again we have A and B and can get our answer to 63568 in its simplest radical form as follows:

√63568 = A√B

√63568 = 4√3973

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