Simplify Square Root of 64512

Here we will show you two methods that you can use to simplify the square root of 64512. In other words, we will show you how to find the square root of 64512 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.

√64512 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 64512 to simplify the square root of 64512. 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 64512. The factors of 64512 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 64, 72, 84, 96, 112, 126, 128, 144, 168, 192, 224, 252, 256, 288, 336, 384, 448, 504, 512, 576, 672, 768, 896, 1008, 1024, 1152, 1344, 1536, 1792, 2016, 2304, 2688, 3072, 3584, 4032, 4608, 5376, 7168, 8064, 9216, 10752, 16128, 21504, 32256, and 64512. Furthermore, the greatest perfect square on this list is 9216 and the square root of 9216 is 96. Therefore, A equals 96.

B = Calculate 64512 divided by the greatest perfect square from the list of all factors of 64512. We determined above that the greatest perfect square from the list of all factors of 64512 is 9216. Furthermore, 64512 divided by 9216 is 7, therefore B equals 7.

Now we have A and B and can get our answer to 64512 in its simplest radical form as follows:

√64512 = A√B

√64512 = 96√7

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 64512 to simplify the square root of 64512 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 64512 and then take the square root of that product. The prime factors that multiply together to make 64512 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 = 9216 and the square root of 9216 is 96. Therefore, A equals 96.

B = Divide 64512 by the number (A) squared. 96 squared is 9216 and 64512 divided by 9216 is 7. Therefore, B equals 7.

Once again we have A and B and can get our answer to 64512 in its simplest radical form as follows:

√64512 = A√B

√64512 = 96√7

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 64513
Here is the next square root on our list that we have simplifed for you.