Simplify Square Root of 73344

Here we will show you two methods that you can use to simplify the square root of 73344. In other words, we will show you how to find the square root of 73344 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.

√73344 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 73344 to simplify the square root of 73344. 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 73344. The factors of 73344 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 191, 192, 382, 384, 573, 764, 1146, 1528, 2292, 3056, 4584, 6112, 9168, 12224, 18336, 24448, 36672, and 73344. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 73344 divided by the greatest perfect square from the list of all factors of 73344. We determined above that the greatest perfect square from the list of all factors of 73344 is 64. Furthermore, 73344 divided by 64 is 1146, therefore B equals 1146.

Now we have A and B and can get our answer to 73344 in its simplest radical form as follows:

√73344 = A√B

√73344 = 8√1146

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 73344 to simplify the square root of 73344 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 73344 and then take the square root of that product. The prime factors that multiply together to make 73344 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 191. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 73344 by the number (A) squared. 8 squared is 64 and 73344 divided by 64 is 1146. Therefore, B equals 1146.

Once again we have A and B and can get our answer to 73344 in its simplest radical form as follows:

√73344 = A√B

√73344 = 8√1146

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

Simplify Square Root of 73345
Here is the next square root on our list that we have simplifed for you.