Simplify Square Root of 72963

Here we will show you two methods that you can use to simplify the square root of 72963. In other words, we will show you how to find the square root of 72963 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.

√72963 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 72963 to simplify the square root of 72963. 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 72963. The factors of 72963 are 1, 3, 9, 11, 33, 67, 99, 121, 201, 363, 603, 737, 1089, 2211, 6633, 8107, 24321, and 72963. Furthermore, the greatest perfect square on this list is 1089 and the square root of 1089 is 33. Therefore, A equals 33.

B = Calculate 72963 divided by the greatest perfect square from the list of all factors of 72963. We determined above that the greatest perfect square from the list of all factors of 72963 is 1089. Furthermore, 72963 divided by 1089 is 67, therefore B equals 67.

Now we have A and B and can get our answer to 72963 in its simplest radical form as follows:

√72963 = A√B

√72963 = 33√67

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 72963 to simplify the square root of 72963 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 72963 and then take the square root of that product. The prime factors that multiply together to make 72963 are 3 x 3 x 11 x 11 x 67. When we strip out the pairs only, we get 3 x 3 x 11 x 11 = 1089 and the square root of 1089 is 33. Therefore, A equals 33.

B = Divide 72963 by the number (A) squared. 33 squared is 1089 and 72963 divided by 1089 is 67. Therefore, B equals 67.

Once again we have A and B and can get our answer to 72963 in its simplest radical form as follows:

√72963 = A√B

√72963 = 33√67

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

Simplify Square Root of 72964
Here is the next square root on our list that we have simplifed for you.