Simplify Square Root of 22743

Here we will show you two methods that you can use to simplify the square root of 22743. In other words, we will show you how to find the square root of 22743 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.

√22743 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 22743 to simplify the square root of 22743. 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 22743. The factors of 22743 are 1, 3, 7, 9, 19, 21, 57, 63, 133, 171, 361, 399, 1083, 1197, 2527, 3249, 7581, and 22743. Furthermore, the greatest perfect square on this list is 3249 and the square root of 3249 is 57. Therefore, A equals 57.

B = Calculate 22743 divided by the greatest perfect square from the list of all factors of 22743. We determined above that the greatest perfect square from the list of all factors of 22743 is 3249. Furthermore, 22743 divided by 3249 is 7, therefore B equals 7.

Now we have A and B and can get our answer to 22743 in its simplest radical form as follows:

√22743 = A√B

√22743 = 57√7

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 22743 to simplify the square root of 22743 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 22743 and then take the square root of that product. The prime factors that multiply together to make 22743 are 3 x 3 x 7 x 19 x 19. When we strip out the pairs only, we get 3 x 3 x 19 x 19 = 3249 and the square root of 3249 is 57. Therefore, A equals 57.

B = Divide 22743 by the number (A) squared. 57 squared is 3249 and 22743 divided by 3249 is 7. Therefore, B equals 7.

Once again we have A and B and can get our answer to 22743 in its simplest radical form as follows:

√22743 = A√B

√22743 = 57√7

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Simplify Square Root of 22744
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