Simplify Square Root of 52332

Here we will show you two methods that you can use to simplify the square root of 52332. In other words, we will show you how to find the square root of 52332 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.

√52332 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 52332 to simplify the square root of 52332. 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 52332. The factors of 52332 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 89, 98, 147, 178, 196, 267, 294, 356, 534, 588, 623, 1068, 1246, 1869, 2492, 3738, 4361, 7476, 8722, 13083, 17444, 26166, and 52332. Furthermore, the greatest perfect square on this list is 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Calculate 52332 divided by the greatest perfect square from the list of all factors of 52332. We determined above that the greatest perfect square from the list of all factors of 52332 is 196. Furthermore, 52332 divided by 196 is 267, therefore B equals 267.

Now we have A and B and can get our answer to 52332 in its simplest radical form as follows:

√52332 = A√B

√52332 = 14√267

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 52332 to simplify the square root of 52332 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 52332 and then take the square root of that product. The prime factors that multiply together to make 52332 are 2 x 2 x 3 x 7 x 7 x 89. When we strip out the pairs only, we get 2 x 2 x 7 x 7 = 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Divide 52332 by the number (A) squared. 14 squared is 196 and 52332 divided by 196 is 267. Therefore, B equals 267.

Once again we have A and B and can get our answer to 52332 in its simplest radical form as follows:

√52332 = A√B

√52332 = 14√267

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

Simplify Square Root of 52333
Here is the next square root on our list that we have simplifed for you.