Simplify Square Root of 50304

Here we will show you two methods that you can use to simplify the square root of 50304. In other words, we will show you how to find the square root of 50304 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.

√50304 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 50304 to simplify the square root of 50304. 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 50304. The factors of 50304 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 131, 192, 262, 384, 393, 524, 786, 1048, 1572, 2096, 3144, 4192, 6288, 8384, 12576, 16768, 25152, and 50304. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 50304 divided by the greatest perfect square from the list of all factors of 50304. We determined above that the greatest perfect square from the list of all factors of 50304 is 64. Furthermore, 50304 divided by 64 is 786, therefore B equals 786.

Now we have A and B and can get our answer to 50304 in its simplest radical form as follows:

√50304 = A√B

√50304 = 8√786

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 50304 to simplify the square root of 50304 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 50304 and then take the square root of that product. The prime factors that multiply together to make 50304 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 131. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 50304 by the number (A) squared. 8 squared is 64 and 50304 divided by 64 is 786. Therefore, B equals 786.

Once again we have A and B and can get our answer to 50304 in its simplest radical form as follows:

√50304 = A√B

√50304 = 8√786

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