Simplify Square Root of 50193

Here we will show you two methods that you can use to simplify the square root of 50193. In other words, we will show you how to find the square root of 50193 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.

√50193 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 50193 to simplify the square root of 50193. 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 50193. The factors of 50193 are 1, 3, 9, 11, 13, 27, 33, 39, 99, 117, 143, 169, 297, 351, 429, 507, 1287, 1521, 1859, 3861, 4563, 5577, 16731, and 50193. Furthermore, the greatest perfect square on this list is 1521 and the square root of 1521 is 39. Therefore, A equals 39.

B = Calculate 50193 divided by the greatest perfect square from the list of all factors of 50193. We determined above that the greatest perfect square from the list of all factors of 50193 is 1521. Furthermore, 50193 divided by 1521 is 33, therefore B equals 33.

Now we have A and B and can get our answer to 50193 in its simplest radical form as follows:

√50193 = A√B

√50193 = 39√33

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 50193 to simplify the square root of 50193 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 50193 and then take the square root of that product. The prime factors that multiply together to make 50193 are 3 x 3 x 3 x 11 x 13 x 13. When we strip out the pairs only, we get 3 x 3 x 13 x 13 = 1521 and the square root of 1521 is 39. Therefore, A equals 39.

B = Divide 50193 by the number (A) squared. 39 squared is 1521 and 50193 divided by 1521 is 33. Therefore, B equals 33.

Once again we have A and B and can get our answer to 50193 in its simplest radical form as follows:

√50193 = A√B

√50193 = 39√33

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Simplify Square Root of 50194
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