Simplify Square Root of 48996

Here we will show you two methods that you can use to simplify the square root of 48996. In other words, we will show you how to find the square root of 48996 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.

√48996 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 48996 to simplify the square root of 48996. 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 48996. The factors of 48996 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 1361, 2722, 4083, 5444, 8166, 12249, 16332, 24498, and 48996. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 48996 divided by the greatest perfect square from the list of all factors of 48996. We determined above that the greatest perfect square from the list of all factors of 48996 is 36. Furthermore, 48996 divided by 36 is 1361, therefore B equals 1361.

Now we have A and B and can get our answer to 48996 in its simplest radical form as follows:

√48996 = A√B

√48996 = 6√1361

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 48996 to simplify the square root of 48996 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 48996 and then take the square root of that product. The prime factors that multiply together to make 48996 are 2 x 2 x 3 x 3 x 1361. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 48996 by the number (A) squared. 6 squared is 36 and 48996 divided by 36 is 1361. Therefore, B equals 1361.

Once again we have A and B and can get our answer to 48996 in its simplest radical form as follows:

√48996 = A√B

√48996 = 6√1361

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