Simplify Square Root of 50941

Here we will show you two methods that you can use to simplify the square root of 50941. In other words, we will show you how to find the square root of 50941 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.

√50941 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 50941 to simplify the square root of 50941. 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 50941. The factors of 50941 are 1, 11, 121, 421, 4631, and 50941. Furthermore, the greatest perfect square on this list is 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Calculate 50941 divided by the greatest perfect square from the list of all factors of 50941. We determined above that the greatest perfect square from the list of all factors of 50941 is 121. Furthermore, 50941 divided by 121 is 421, therefore B equals 421.

Now we have A and B and can get our answer to 50941 in its simplest radical form as follows:

√50941 = A√B

√50941 = 11√421

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 50941 to simplify the square root of 50941 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 50941 and then take the square root of that product. The prime factors that multiply together to make 50941 are 11 x 11 x 421. When we strip out the pairs only, we get 11 x 11 = 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Divide 50941 by the number (A) squared. 11 squared is 121 and 50941 divided by 121 is 421. Therefore, B equals 421.

Once again we have A and B and can get our answer to 50941 in its simplest radical form as follows:

√50941 = A√B

√50941 = 11√421

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Simplify Square Root of 50942
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