Simplify Square Root of 39618

Here we will show you two methods that you can use to simplify the square root of 39618. In other words, we will show you how to find the square root of 39618 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.

√39618 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39618 to simplify the square root of 39618. 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 39618. The factors of 39618 are 1, 2, 3, 6, 9, 18, 31, 62, 71, 93, 142, 186, 213, 279, 426, 558, 639, 1278, 2201, 4402, 6603, 13206, 19809, and 39618. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 39618 divided by the greatest perfect square from the list of all factors of 39618. We determined above that the greatest perfect square from the list of all factors of 39618 is 9. Furthermore, 39618 divided by 9 is 4402, therefore B equals 4402.

Now we have A and B and can get our answer to 39618 in its simplest radical form as follows:

√39618 = A√B

√39618 = 3√4402

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39618 to simplify the square root of 39618 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 39618 and then take the square root of that product. The prime factors that multiply together to make 39618 are 2 x 3 x 3 x 31 x 71. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 39618 by the number (A) squared. 3 squared is 9 and 39618 divided by 9 is 4402. Therefore, B equals 4402.

Once again we have A and B and can get our answer to 39618 in its simplest radical form as follows:

√39618 = A√B

√39618 = 3√4402

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