Simplify Square Root of 51714

Here we will show you two methods that you can use to simplify the square root of 51714. In other words, we will show you how to find the square root of 51714 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.

√51714 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 51714 to simplify the square root of 51714. 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 51714. The factors of 51714 are 1, 2, 3, 6, 9, 13, 17, 18, 26, 34, 39, 51, 78, 102, 117, 153, 169, 221, 234, 306, 338, 442, 507, 663, 1014, 1326, 1521, 1989, 2873, 3042, 3978, 5746, 8619, 17238, 25857, and 51714. Furthermore, the greatest perfect square on this list is 1521 and the square root of 1521 is 39. Therefore, A equals 39.

B = Calculate 51714 divided by the greatest perfect square from the list of all factors of 51714. We determined above that the greatest perfect square from the list of all factors of 51714 is 1521. Furthermore, 51714 divided by 1521 is 34, therefore B equals 34.

Now we have A and B and can get our answer to 51714 in its simplest radical form as follows:

√51714 = A√B

√51714 = 39√34

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 51714 to simplify the square root of 51714 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 51714 and then take the square root of that product. The prime factors that multiply together to make 51714 are 2 x 3 x 3 x 13 x 13 x 17. When we strip out the pairs only, we get 3 x 3 x 13 x 13 = 1521 and the square root of 1521 is 39. Therefore, A equals 39.

B = Divide 51714 by the number (A) squared. 39 squared is 1521 and 51714 divided by 1521 is 34. Therefore, B equals 34.

Once again we have A and B and can get our answer to 51714 in its simplest radical form as follows:

√51714 = A√B

√51714 = 39√34

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

Simplify Square Root of 51715
Here is the next square root on our list that we have simplifed for you.