Simplify Square Root of 50832

Here we will show you two methods that you can use to simplify the square root of 50832. In other words, we will show you how to find the square root of 50832 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.

√50832 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 50832 to simplify the square root of 50832. 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 50832. The factors of 50832 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 353, 706, 1059, 1412, 2118, 2824, 3177, 4236, 5648, 6354, 8472, 12708, 16944, 25416, and 50832. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 50832 divided by the greatest perfect square from the list of all factors of 50832. We determined above that the greatest perfect square from the list of all factors of 50832 is 144. Furthermore, 50832 divided by 144 is 353, therefore B equals 353.

Now we have A and B and can get our answer to 50832 in its simplest radical form as follows:

√50832 = A√B

√50832 = 12√353

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 50832 to simplify the square root of 50832 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 50832 and then take the square root of that product. The prime factors that multiply together to make 50832 are 2 x 2 x 2 x 2 x 3 x 3 x 353. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 = 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Divide 50832 by the number (A) squared. 12 squared is 144 and 50832 divided by 144 is 353. Therefore, B equals 353.

Once again we have A and B and can get our answer to 50832 in its simplest radical form as follows:

√50832 = A√B

√50832 = 12√353

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Simplify Square Root of 50833
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