Simplify Square Root of 34656

Here we will show you two methods that you can use to simplify the square root of 34656. In other words, we will show you how to find the square root of 34656 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.

√34656 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 34656 to simplify the square root of 34656. 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 34656. The factors of 34656 are 1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 76, 96, 114, 152, 228, 304, 361, 456, 608, 722, 912, 1083, 1444, 1824, 2166, 2888, 4332, 5776, 8664, 11552, 17328, and 34656. Furthermore, the greatest perfect square on this list is 5776 and the square root of 5776 is 76. Therefore, A equals 76.

B = Calculate 34656 divided by the greatest perfect square from the list of all factors of 34656. We determined above that the greatest perfect square from the list of all factors of 34656 is 5776. Furthermore, 34656 divided by 5776 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 34656 in its simplest radical form as follows:

√34656 = A√B

√34656 = 76√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 34656 to simplify the square root of 34656 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 34656 and then take the square root of that product. The prime factors that multiply together to make 34656 are 2 x 2 x 2 x 2 x 2 x 3 x 19 x 19. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 19 x 19 = 5776 and the square root of 5776 is 76. Therefore, A equals 76.

B = Divide 34656 by the number (A) squared. 76 squared is 5776 and 34656 divided by 5776 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 34656 in its simplest radical form as follows:

√34656 = A√B

√34656 = 76√6

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