Simplify Square Root of 50700

Here we will show you two methods that you can use to simplify the square root of 50700. In other words, we will show you how to find the square root of 50700 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.

√50700 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 50700 to simplify the square root of 50700. 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 50700. The factors of 50700 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 25, 26, 30, 39, 50, 52, 60, 65, 75, 78, 100, 130, 150, 156, 169, 195, 260, 300, 325, 338, 390, 507, 650, 676, 780, 845, 975, 1014, 1300, 1690, 1950, 2028, 2535, 3380, 3900, 4225, 5070, 8450, 10140, 12675, 16900, 25350, and 50700. Furthermore, the greatest perfect square on this list is 16900 and the square root of 16900 is 130. Therefore, A equals 130.

B = Calculate 50700 divided by the greatest perfect square from the list of all factors of 50700. We determined above that the greatest perfect square from the list of all factors of 50700 is 16900. Furthermore, 50700 divided by 16900 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 50700 in its simplest radical form as follows:

√50700 = A√B

√50700 = 130√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 50700 to simplify the square root of 50700 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 50700 and then take the square root of that product. The prime factors that multiply together to make 50700 are 2 x 2 x 3 x 5 x 5 x 13 x 13. When we strip out the pairs only, we get 2 x 2 x 5 x 5 x 13 x 13 = 16900 and the square root of 16900 is 130. Therefore, A equals 130.

B = Divide 50700 by the number (A) squared. 130 squared is 16900 and 50700 divided by 16900 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 50700 in its simplest radical form as follows:

√50700 = A√B

√50700 = 130√3

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

Simplify Square Root of 50701
Here is the next square root on our list that we have simplifed for you.