Simplify Square Root of 7290

Here we will show you two methods that you can use to simplify the square root of 7290. In other words, we will show you how to find the square root of 7290 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.

√7290 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 7290 to simplify the square root of 7290. 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 7290. The factors of 7290 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 729, 810, 1215, 1458, 2430, 3645, and 7290. Furthermore, the greatest perfect square on this list is 729 and the square root of 729 is 27. Therefore, A equals 27.

B = Calculate 7290 divided by the greatest perfect square from the list of all factors of 7290. We determined above that the greatest perfect square from the list of all factors of 7290 is 729. Furthermore, 7290 divided by 729 is 10, therefore B equals 10.

Now we have A and B and can get our answer to 7290 in its simplest radical form as follows:

√7290 = A√B

√7290 = 27√10

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 7290 to simplify the square root of 7290 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 7290 and then take the square root of that product. The prime factors that multiply together to make 7290 are 2 x 3 x 3 x 3 x 3 x 3 x 3 x 5. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 3 x 3 = 729 and the square root of 729 is 27. Therefore, A equals 27.

B = Divide 7290 by the number (A) squared. 27 squared is 729 and 7290 divided by 729 is 10. Therefore, B equals 10.

Once again we have A and B and can get our answer to 7290 in its simplest radical form as follows:

√7290 = A√B

√7290 = 27√10

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

Simplify Square Root of 7291
Here is the next square root on our list that we have simplifed for you.