Simplify Square Root of 54738

Here we will show you two methods that you can use to simplify the square root of 54738. In other words, we will show you how to find the square root of 54738 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.

√54738 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 54738 to simplify the square root of 54738. 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 54738. The factors of 54738 are 1, 2, 3, 6, 9, 18, 3041, 6082, 9123, 18246, 27369, and 54738. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 54738 divided by the greatest perfect square from the list of all factors of 54738. We determined above that the greatest perfect square from the list of all factors of 54738 is 9. Furthermore, 54738 divided by 9 is 6082, therefore B equals 6082.

Now we have A and B and can get our answer to 54738 in its simplest radical form as follows:

√54738 = A√B

√54738 = 3√6082

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 54738 to simplify the square root of 54738 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 54738 and then take the square root of that product. The prime factors that multiply together to make 54738 are 2 x 3 x 3 x 3041. 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 54738 by the number (A) squared. 3 squared is 9 and 54738 divided by 9 is 6082. Therefore, B equals 6082.

Once again we have A and B and can get our answer to 54738 in its simplest radical form as follows:

√54738 = A√B

√54738 = 3√6082

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

Simplify Square Root of 54739
Here is the next square root on our list that we have simplifed for you.