Simplify Square Root of 12654

Here we will show you two methods that you can use to simplify the square root of 12654. In other words, we will show you how to find the square root of 12654 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.

√12654 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 12654 to simplify the square root of 12654. 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 12654. The factors of 12654 are 1, 2, 3, 6, 9, 18, 19, 37, 38, 57, 74, 111, 114, 171, 222, 333, 342, 666, 703, 1406, 2109, 4218, 6327, and 12654. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 12654 divided by the greatest perfect square from the list of all factors of 12654. We determined above that the greatest perfect square from the list of all factors of 12654 is 9. Furthermore, 12654 divided by 9 is 1406, therefore B equals 1406.

Now we have A and B and can get our answer to 12654 in its simplest radical form as follows:

√12654 = A√B

√12654 = 3√1406

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 12654 to simplify the square root of 12654 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 12654 and then take the square root of that product. The prime factors that multiply together to make 12654 are 2 x 3 x 3 x 19 x 37. 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 12654 by the number (A) squared. 3 squared is 9 and 12654 divided by 9 is 1406. Therefore, B equals 1406.

Once again we have A and B and can get our answer to 12654 in its simplest radical form as follows:

√12654 = A√B

√12654 = 3√1406

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 12655
Here is the next square root on our list that we have simplifed for you.