Simplify Square Root of 58824

Here we will show you two methods that you can use to simplify the square root of 58824. In other words, we will show you how to find the square root of 58824 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.

√58824 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 58824 to simplify the square root of 58824. 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 58824. The factors of 58824 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 19, 24, 36, 38, 43, 57, 72, 76, 86, 114, 129, 152, 171, 172, 228, 258, 342, 344, 387, 456, 516, 684, 774, 817, 1032, 1368, 1548, 1634, 2451, 3096, 3268, 4902, 6536, 7353, 9804, 14706, 19608, 29412, and 58824. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 58824 divided by the greatest perfect square from the list of all factors of 58824. We determined above that the greatest perfect square from the list of all factors of 58824 is 36. Furthermore, 58824 divided by 36 is 1634, therefore B equals 1634.

Now we have A and B and can get our answer to 58824 in its simplest radical form as follows:

√58824 = A√B

√58824 = 6√1634

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 58824 to simplify the square root of 58824 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 58824 and then take the square root of that product. The prime factors that multiply together to make 58824 are 2 x 2 x 2 x 3 x 3 x 19 x 43. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 58824 by the number (A) squared. 6 squared is 36 and 58824 divided by 36 is 1634. Therefore, B equals 1634.

Once again we have A and B and can get our answer to 58824 in its simplest radical form as follows:

√58824 = A√B

√58824 = 6√1634

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Simplify Square Root of 58825
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