Simplify Square Root of 1632

Here we will show you two methods that you can use to simplify the square root of 1632. In other words, we will show you how to find the square root of 1632 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.

√1632 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 1632 to simplify the square root of 1632. 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 1632. The factors of 1632 are 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 32, 34, 48, 51, 68, 96, 102, 136, 204, 272, 408, 544, 816, and 1632. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 1632 divided by the greatest perfect square from the list of all factors of 1632. We determined above that the greatest perfect square from the list of all factors of 1632 is 16. Furthermore, 1632 divided by 16 is 102, therefore B equals 102.

Now we have A and B and can get our answer to 1632 in its simplest radical form as follows:

√1632 = A√B

√1632 = 4√102

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 1632 to simplify the square root of 1632 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 1632 and then take the square root of that product. The prime factors that multiply together to make 1632 are 2 x 2 x 2 x 2 x 2 x 3 x 17. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 1632 by the number (A) squared. 4 squared is 16 and 1632 divided by 16 is 102. Therefore, B equals 102.

Once again we have A and B and can get our answer to 1632 in its simplest radical form as follows:

√1632 = A√B

√1632 = 4√102

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

Simplify Square Root of 1633
Here is the next square root on our list that we have simplifed for you.