Simplify Square Root of 50901

Here we will show you two methods that you can use to simplify the square root of 50901. In other words, we will show you how to find the square root of 50901 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.

√50901 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 50901 to simplify the square root of 50901. 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 50901. The factors of 50901 are 1, 3, 19, 47, 57, 141, 361, 893, 1083, 2679, 16967, and 50901. Furthermore, the greatest perfect square on this list is 361 and the square root of 361 is 19. Therefore, A equals 19.

B = Calculate 50901 divided by the greatest perfect square from the list of all factors of 50901. We determined above that the greatest perfect square from the list of all factors of 50901 is 361. Furthermore, 50901 divided by 361 is 141, therefore B equals 141.

Now we have A and B and can get our answer to 50901 in its simplest radical form as follows:

√50901 = A√B

√50901 = 19√141

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 50901 to simplify the square root of 50901 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 50901 and then take the square root of that product. The prime factors that multiply together to make 50901 are 3 x 19 x 19 x 47. When we strip out the pairs only, we get 19 x 19 = 361 and the square root of 361 is 19. Therefore, A equals 19.

B = Divide 50901 by the number (A) squared. 19 squared is 361 and 50901 divided by 361 is 141. Therefore, B equals 141.

Once again we have A and B and can get our answer to 50901 in its simplest radical form as follows:

√50901 = A√B

√50901 = 19√141

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