Simplify Square Root of 27075

Here we will show you two methods that you can use to simplify the square root of 27075. In other words, we will show you how to find the square root of 27075 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.

√27075 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 27075 to simplify the square root of 27075. 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 27075. The factors of 27075 are 1, 3, 5, 15, 19, 25, 57, 75, 95, 285, 361, 475, 1083, 1425, 1805, 5415, 9025, and 27075. Furthermore, the greatest perfect square on this list is 9025 and the square root of 9025 is 95. Therefore, A equals 95.

B = Calculate 27075 divided by the greatest perfect square from the list of all factors of 27075. We determined above that the greatest perfect square from the list of all factors of 27075 is 9025. Furthermore, 27075 divided by 9025 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 27075 in its simplest radical form as follows:

√27075 = A√B

√27075 = 95√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 27075 to simplify the square root of 27075 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 27075 and then take the square root of that product. The prime factors that multiply together to make 27075 are 3 x 5 x 5 x 19 x 19. When we strip out the pairs only, we get 5 x 5 x 19 x 19 = 9025 and the square root of 9025 is 95. Therefore, A equals 95.

B = Divide 27075 by the number (A) squared. 95 squared is 9025 and 27075 divided by 9025 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 27075 in its simplest radical form as follows:

√27075 = A√B

√27075 = 95√3

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

Simplify Square Root of 27076
Here is the next square root on our list that we have simplifed for you.