Simplify Square Root of 30618

Here we will show you two methods that you can use to simplify the square root of 30618. In other words, we will show you how to find the square root of 30618 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.

√30618 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 30618 to simplify the square root of 30618. 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 30618. The factors of 30618 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 81, 126, 162, 189, 243, 378, 486, 567, 729, 1134, 1458, 1701, 2187, 3402, 4374, 5103, 10206, 15309, and 30618. Furthermore, the greatest perfect square on this list is 729 and the square root of 729 is 27. Therefore, A equals 27.

B = Calculate 30618 divided by the greatest perfect square from the list of all factors of 30618. We determined above that the greatest perfect square from the list of all factors of 30618 is 729. Furthermore, 30618 divided by 729 is 42, therefore B equals 42.

Now we have A and B and can get our answer to 30618 in its simplest radical form as follows:

√30618 = A√B

√30618 = 27√42

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 30618 to simplify the square root of 30618 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 30618 and then take the square root of that product. The prime factors that multiply together to make 30618 are 2 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 7. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 3 x 3 = 729 and the square root of 729 is 27. Therefore, A equals 27.

B = Divide 30618 by the number (A) squared. 27 squared is 729 and 30618 divided by 729 is 42. Therefore, B equals 42.

Once again we have A and B and can get our answer to 30618 in its simplest radical form as follows:

√30618 = A√B

√30618 = 27√42

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