Simplify Square Root of 3150

Here we will show you two methods that you can use to simplify the square root of 3150. In other words, we will show you how to find the square root of 3150 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.

√3150 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 3150 to simplify the square root of 3150. 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 3150. The factors of 3150 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 25, 30, 35, 42, 45, 50, 63, 70, 75, 90, 105, 126, 150, 175, 210, 225, 315, 350, 450, 525, 630, 1050, 1575, and 3150. Furthermore, the greatest perfect square on this list is 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Calculate 3150 divided by the greatest perfect square from the list of all factors of 3150. We determined above that the greatest perfect square from the list of all factors of 3150 is 225. Furthermore, 3150 divided by 225 is 14, therefore B equals 14.

Now we have A and B and can get our answer to 3150 in its simplest radical form as follows:

√3150 = A√B

√3150 = 15√14

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 3150 to simplify the square root of 3150 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 3150 and then take the square root of that product. The prime factors that multiply together to make 3150 are 2 x 3 x 3 x 5 x 5 x 7. When we strip out the pairs only, we get 3 x 3 x 5 x 5 = 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Divide 3150 by the number (A) squared. 15 squared is 225 and 3150 divided by 225 is 14. Therefore, B equals 14.

Once again we have A and B and can get our answer to 3150 in its simplest radical form as follows:

√3150 = A√B

√3150 = 15√14

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

Simplify Square Root of 3151
Here is the next square root on our list that we have simplifed for you.