Simplify Square Root of 30656

Here we will show you two methods that you can use to simplify the square root of 30656. In other words, we will show you how to find the square root of 30656 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.

√30656 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 30656 to simplify the square root of 30656. 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 30656. The factors of 30656 are 1, 2, 4, 8, 16, 32, 64, 479, 958, 1916, 3832, 7664, 15328, and 30656. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 30656 divided by the greatest perfect square from the list of all factors of 30656. We determined above that the greatest perfect square from the list of all factors of 30656 is 64. Furthermore, 30656 divided by 64 is 479, therefore B equals 479.

Now we have A and B and can get our answer to 30656 in its simplest radical form as follows:

√30656 = A√B

√30656 = 8√479

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 30656 to simplify the square root of 30656 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 30656 and then take the square root of that product. The prime factors that multiply together to make 30656 are 2 x 2 x 2 x 2 x 2 x 2 x 479. 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 30656 by the number (A) squared. 8 squared is 64 and 30656 divided by 64 is 479. Therefore, B equals 479.

Once again we have A and B and can get our answer to 30656 in its simplest radical form as follows:

√30656 = A√B

√30656 = 8√479

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Simplify Square Root of 30657
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