Simplify Square Root of 90144

Here we will show you two methods that you can use to simplify the square root of 90144. In other words, we will show you how to find the square root of 90144 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.

√90144 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 90144 to simplify the square root of 90144. 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 90144. The factors of 90144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288, 313, 626, 939, 1252, 1878, 2504, 2817, 3756, 5008, 5634, 7512, 10016, 11268, 15024, 22536, 30048, 45072, and 90144. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 90144 divided by the greatest perfect square from the list of all factors of 90144. We determined above that the greatest perfect square from the list of all factors of 90144 is 144. Furthermore, 90144 divided by 144 is 626, therefore B equals 626.

Now we have A and B and can get our answer to 90144 in its simplest radical form as follows:

√90144 = A√B

√90144 = 12√626

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 90144 to simplify the square root of 90144 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 90144 and then take the square root of that product. The prime factors that multiply together to make 90144 are 2 x 2 x 2 x 2 x 2 x 3 x 3 x 313. 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 90144 by the number (A) squared. 12 squared is 144 and 90144 divided by 144 is 626. Therefore, B equals 626.

Once again we have A and B and can get our answer to 90144 in its simplest radical form as follows:

√90144 = A√B

√90144 = 12√626

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

Simplify Square Root of 90145
Here is the next square root on our list that we have simplifed for you.