Simplify Square Root of 50823

Here we will show you two methods that you can use to simplify the square root of 50823. In other words, we will show you how to find the square root of 50823 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.

√50823 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 50823 to simplify the square root of 50823. 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 50823. The factors of 50823 are 1, 3, 9, 5647, 16941, and 50823. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 50823 divided by the greatest perfect square from the list of all factors of 50823. We determined above that the greatest perfect square from the list of all factors of 50823 is 9. Furthermore, 50823 divided by 9 is 5647, therefore B equals 5647.

Now we have A and B and can get our answer to 50823 in its simplest radical form as follows:

√50823 = A√B

√50823 = 3√5647

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 50823 to simplify the square root of 50823 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 50823 and then take the square root of that product. The prime factors that multiply together to make 50823 are 3 x 3 x 5647. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 50823 by the number (A) squared. 3 squared is 9 and 50823 divided by 9 is 5647. Therefore, B equals 5647.

Once again we have A and B and can get our answer to 50823 in its simplest radical form as follows:

√50823 = A√B

√50823 = 3√5647

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