Simplify Square Root of 65664

Here we will show you two methods that you can use to simplify the square root of 65664. In other words, we will show you how to find the square root of 65664 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.

√65664 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 65664 to simplify the square root of 65664. 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 65664. The factors of 65664 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 27, 32, 36, 38, 48, 54, 57, 64, 72, 76, 96, 108, 114, 128, 144, 152, 171, 192, 216, 228, 288, 304, 342, 384, 432, 456, 513, 576, 608, 684, 864, 912, 1026, 1152, 1216, 1368, 1728, 1824, 2052, 2432, 2736, 3456, 3648, 4104, 5472, 7296, 8208, 10944, 16416, 21888, 32832, and 65664. Furthermore, the greatest perfect square on this list is 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Calculate 65664 divided by the greatest perfect square from the list of all factors of 65664. We determined above that the greatest perfect square from the list of all factors of 65664 is 576. Furthermore, 65664 divided by 576 is 114, therefore B equals 114.

Now we have A and B and can get our answer to 65664 in its simplest radical form as follows:

√65664 = A√B

√65664 = 24√114

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 65664 to simplify the square root of 65664 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 65664 and then take the square root of that product. The prime factors that multiply together to make 65664 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 19. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 = 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Divide 65664 by the number (A) squared. 24 squared is 576 and 65664 divided by 576 is 114. Therefore, B equals 114.

Once again we have A and B and can get our answer to 65664 in its simplest radical form as follows:

√65664 = A√B

√65664 = 24√114

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