Simplify Square Root of 40824

Here we will show you two methods that you can use to simplify the square root of 40824. In other words, we will show you how to find the square root of 40824 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.

√40824 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 40824 to simplify the square root of 40824. 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 40824. The factors of 40824 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 81, 84, 108, 126, 162, 168, 189, 216, 243, 252, 324, 378, 486, 504, 567, 648, 729, 756, 972, 1134, 1458, 1512, 1701, 1944, 2268, 2916, 3402, 4536, 5103, 5832, 6804, 10206, 13608, 20412, and 40824. Furthermore, the greatest perfect square on this list is 2916 and the square root of 2916 is 54. Therefore, A equals 54.

B = Calculate 40824 divided by the greatest perfect square from the list of all factors of 40824. We determined above that the greatest perfect square from the list of all factors of 40824 is 2916. Furthermore, 40824 divided by 2916 is 14, therefore B equals 14.

Now we have A and B and can get our answer to 40824 in its simplest radical form as follows:

√40824 = A√B

√40824 = 54√14

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 40824 to simplify the square root of 40824 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 40824 and then take the square root of that product. The prime factors that multiply together to make 40824 are 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 x 7. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 = 2916 and the square root of 2916 is 54. Therefore, A equals 54.

B = Divide 40824 by the number (A) squared. 54 squared is 2916 and 40824 divided by 2916 is 14. Therefore, B equals 14.

Once again we have A and B and can get our answer to 40824 in its simplest radical form as follows:

√40824 = A√B

√40824 = 54√14

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Simplify Square Root of 40825
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