Simplify Square Root of 50933

Here we will show you two methods that you can use to simplify the square root of 50933. In other words, we will show you how to find the square root of 50933 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.

√50933 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 50933 to simplify the square root of 50933. 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 50933. The factors of 50933 are 1, 31, 53, 961, 1643, and 50933. Furthermore, the greatest perfect square on this list is 961 and the square root of 961 is 31. Therefore, A equals 31.

B = Calculate 50933 divided by the greatest perfect square from the list of all factors of 50933. We determined above that the greatest perfect square from the list of all factors of 50933 is 961. Furthermore, 50933 divided by 961 is 53, therefore B equals 53.

Now we have A and B and can get our answer to 50933 in its simplest radical form as follows:

√50933 = A√B

√50933 = 31√53

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 50933 to simplify the square root of 50933 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 50933 and then take the square root of that product. The prime factors that multiply together to make 50933 are 31 x 31 x 53. When we strip out the pairs only, we get 31 x 31 = 961 and the square root of 961 is 31. Therefore, A equals 31.

B = Divide 50933 by the number (A) squared. 31 squared is 961 and 50933 divided by 961 is 53. Therefore, B equals 53.

Once again we have A and B and can get our answer to 50933 in its simplest radical form as follows:

√50933 = A√B

√50933 = 31√53

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Simplify Square Root of 50934
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