Simplify Square Root of 21024

Here we will show you two methods that you can use to simplify the square root of 21024. In other words, we will show you how to find the square root of 21024 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.

√21024 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 21024 to simplify the square root of 21024. 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 21024. The factors of 21024 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 73, 96, 144, 146, 219, 288, 292, 438, 584, 657, 876, 1168, 1314, 1752, 2336, 2628, 3504, 5256, 7008, 10512, and 21024. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 21024 divided by the greatest perfect square from the list of all factors of 21024. We determined above that the greatest perfect square from the list of all factors of 21024 is 144. Furthermore, 21024 divided by 144 is 146, therefore B equals 146.

Now we have A and B and can get our answer to 21024 in its simplest radical form as follows:

√21024 = A√B

√21024 = 12√146

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 21024 to simplify the square root of 21024 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 21024 and then take the square root of that product. The prime factors that multiply together to make 21024 are 2 x 2 x 2 x 2 x 2 x 3 x 3 x 73. 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 21024 by the number (A) squared. 12 squared is 144 and 21024 divided by 144 is 146. Therefore, B equals 146.

Once again we have A and B and can get our answer to 21024 in its simplest radical form as follows:

√21024 = A√B

√21024 = 12√146

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

Simplify Square Root of 21025
Here is the next square root on our list that we have simplifed for you.