Simplify Square Root of 49968

Here we will show you two methods that you can use to simplify the square root of 49968. In other words, we will show you how to find the square root of 49968 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.

√49968 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 49968 to simplify the square root of 49968. 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 49968. The factors of 49968 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 347, 694, 1041, 1388, 2082, 2776, 3123, 4164, 5552, 6246, 8328, 12492, 16656, 24984, and 49968. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 49968 divided by the greatest perfect square from the list of all factors of 49968. We determined above that the greatest perfect square from the list of all factors of 49968 is 144. Furthermore, 49968 divided by 144 is 347, therefore B equals 347.

Now we have A and B and can get our answer to 49968 in its simplest radical form as follows:

√49968 = A√B

√49968 = 12√347

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 49968 to simplify the square root of 49968 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 49968 and then take the square root of that product. The prime factors that multiply together to make 49968 are 2 x 2 x 2 x 2 x 3 x 3 x 347. 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 49968 by the number (A) squared. 12 squared is 144 and 49968 divided by 144 is 347. Therefore, B equals 347.

Once again we have A and B and can get our answer to 49968 in its simplest radical form as follows:

√49968 = A√B

√49968 = 12√347

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Simplify Square Root of 49969
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