Simplify Square Root of 57664

Here we will show you two methods that you can use to simplify the square root of 57664. In other words, we will show you how to find the square root of 57664 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.

√57664 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 57664 to simplify the square root of 57664. 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 57664. The factors of 57664 are 1, 2, 4, 8, 16, 17, 32, 34, 53, 64, 68, 106, 136, 212, 272, 424, 544, 848, 901, 1088, 1696, 1802, 3392, 3604, 7208, 14416, 28832, and 57664. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 57664 divided by the greatest perfect square from the list of all factors of 57664. We determined above that the greatest perfect square from the list of all factors of 57664 is 64. Furthermore, 57664 divided by 64 is 901, therefore B equals 901.

Now we have A and B and can get our answer to 57664 in its simplest radical form as follows:

√57664 = A√B

√57664 = 8√901

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 57664 to simplify the square root of 57664 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 57664 and then take the square root of that product. The prime factors that multiply together to make 57664 are 2 x 2 x 2 x 2 x 2 x 2 x 17 x 53. 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 57664 by the number (A) squared. 8 squared is 64 and 57664 divided by 64 is 901. Therefore, B equals 901.

Once again we have A and B and can get our answer to 57664 in its simplest radical form as follows:

√57664 = A√B

√57664 = 8√901

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Simplify Square Root of 57665
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