Simplify Square Root of 49527

Here we will show you two methods that you can use to simplify the square root of 49527. In other words, we will show you how to find the square root of 49527 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.

√49527 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 49527 to simplify the square root of 49527. 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 49527. The factors of 49527 are 1, 3, 9, 5503, 16509, and 49527. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 49527 divided by the greatest perfect square from the list of all factors of 49527. We determined above that the greatest perfect square from the list of all factors of 49527 is 9. Furthermore, 49527 divided by 9 is 5503, therefore B equals 5503.

Now we have A and B and can get our answer to 49527 in its simplest radical form as follows:

√49527 = A√B

√49527 = 3√5503

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 49527 to simplify the square root of 49527 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 49527 and then take the square root of that product. The prime factors that multiply together to make 49527 are 3 x 3 x 5503. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 49527 by the number (A) squared. 3 squared is 9 and 49527 divided by 9 is 5503. Therefore, B equals 5503.

Once again we have A and B and can get our answer to 49527 in its simplest radical form as follows:

√49527 = A√B

√49527 = 3√5503

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

Simplify Square Root of 49528
Here is the next square root on our list that we have simplifed for you.