Simplify Square Root of 50094

Here we will show you two methods that you can use to simplify the square root of 50094. In other words, we will show you how to find the square root of 50094 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.

√50094 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 50094 to simplify the square root of 50094. 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 50094. The factors of 50094 are 1, 2, 3, 6, 9, 11, 18, 22, 23, 33, 46, 66, 69, 99, 121, 138, 198, 207, 242, 253, 363, 414, 506, 726, 759, 1089, 1518, 2178, 2277, 2783, 4554, 5566, 8349, 16698, 25047, and 50094. Furthermore, the greatest perfect square on this list is 1089 and the square root of 1089 is 33. Therefore, A equals 33.

B = Calculate 50094 divided by the greatest perfect square from the list of all factors of 50094. We determined above that the greatest perfect square from the list of all factors of 50094 is 1089. Furthermore, 50094 divided by 1089 is 46, therefore B equals 46.

Now we have A and B and can get our answer to 50094 in its simplest radical form as follows:

√50094 = A√B

√50094 = 33√46

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 50094 to simplify the square root of 50094 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 50094 and then take the square root of that product. The prime factors that multiply together to make 50094 are 2 x 3 x 3 x 11 x 11 x 23. When we strip out the pairs only, we get 3 x 3 x 11 x 11 = 1089 and the square root of 1089 is 33. Therefore, A equals 33.

B = Divide 50094 by the number (A) squared. 33 squared is 1089 and 50094 divided by 1089 is 46. Therefore, B equals 46.

Once again we have A and B and can get our answer to 50094 in its simplest radical form as follows:

√50094 = A√B

√50094 = 33√46

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