Simplify Square Root of 30960

Here we will show you two methods that you can use to simplify the square root of 30960. In other words, we will show you how to find the square root of 30960 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.

√30960 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 30960 to simplify the square root of 30960. 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 30960. The factors of 30960 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 43, 45, 48, 60, 72, 80, 86, 90, 120, 129, 144, 172, 180, 215, 240, 258, 344, 360, 387, 430, 516, 645, 688, 720, 774, 860, 1032, 1290, 1548, 1720, 1935, 2064, 2580, 3096, 3440, 3870, 5160, 6192, 7740, 10320, 15480, and 30960. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 30960 divided by the greatest perfect square from the list of all factors of 30960. We determined above that the greatest perfect square from the list of all factors of 30960 is 144. Furthermore, 30960 divided by 144 is 215, therefore B equals 215.

Now we have A and B and can get our answer to 30960 in its simplest radical form as follows:

√30960 = A√B

√30960 = 12√215

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 30960 to simplify the square root of 30960 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 30960 and then take the square root of that product. The prime factors that multiply together to make 30960 are 2 x 2 x 2 x 2 x 3 x 3 x 5 x 43. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 = 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Divide 30960 by the number (A) squared. 12 squared is 144 and 30960 divided by 144 is 215. Therefore, B equals 215.

Once again we have A and B and can get our answer to 30960 in its simplest radical form as follows:

√30960 = A√B

√30960 = 12√215

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Simplify Square Root of 30961
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