Simplify Square Root of 89082

Here we will show you two methods that you can use to simplify the square root of 89082. In other words, we will show you how to find the square root of 89082 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.

√89082 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 89082 to simplify the square root of 89082. 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 89082. The factors of 89082 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 101, 126, 147, 202, 294, 303, 441, 606, 707, 882, 909, 1414, 1818, 2121, 4242, 4949, 6363, 9898, 12726, 14847, 29694, 44541, and 89082. Furthermore, the greatest perfect square on this list is 441 and the square root of 441 is 21. Therefore, A equals 21.

B = Calculate 89082 divided by the greatest perfect square from the list of all factors of 89082. We determined above that the greatest perfect square from the list of all factors of 89082 is 441. Furthermore, 89082 divided by 441 is 202, therefore B equals 202.

Now we have A and B and can get our answer to 89082 in its simplest radical form as follows:

√89082 = A√B

√89082 = 21√202

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 89082 to simplify the square root of 89082 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 89082 and then take the square root of that product. The prime factors that multiply together to make 89082 are 2 x 3 x 3 x 7 x 7 x 101. When we strip out the pairs only, we get 3 x 3 x 7 x 7 = 441 and the square root of 441 is 21. Therefore, A equals 21.

B = Divide 89082 by the number (A) squared. 21 squared is 441 and 89082 divided by 441 is 202. Therefore, B equals 202.

Once again we have A and B and can get our answer to 89082 in its simplest radical form as follows:

√89082 = A√B

√89082 = 21√202

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

Simplify Square Root of 89083
Here is the next square root on our list that we have simplifed for you.