Simplify Square Root of 58812

Here we will show you two methods that you can use to simplify the square root of 58812. In other words, we will show you how to find the square root of 58812 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.

√58812 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 58812 to simplify the square root of 58812. 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 58812. The factors of 58812 are 1, 2, 3, 4, 6, 12, 13, 26, 29, 39, 52, 58, 78, 87, 116, 156, 169, 174, 338, 348, 377, 507, 676, 754, 1014, 1131, 1508, 2028, 2262, 4524, 4901, 9802, 14703, 19604, 29406, and 58812. Furthermore, the greatest perfect square on this list is 676 and the square root of 676 is 26. Therefore, A equals 26.

B = Calculate 58812 divided by the greatest perfect square from the list of all factors of 58812. We determined above that the greatest perfect square from the list of all factors of 58812 is 676. Furthermore, 58812 divided by 676 is 87, therefore B equals 87.

Now we have A and B and can get our answer to 58812 in its simplest radical form as follows:

√58812 = A√B

√58812 = 26√87

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 58812 to simplify the square root of 58812 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 58812 and then take the square root of that product. The prime factors that multiply together to make 58812 are 2 x 2 x 3 x 13 x 13 x 29. When we strip out the pairs only, we get 2 x 2 x 13 x 13 = 676 and the square root of 676 is 26. Therefore, A equals 26.

B = Divide 58812 by the number (A) squared. 26 squared is 676 and 58812 divided by 676 is 87. Therefore, B equals 87.

Once again we have A and B and can get our answer to 58812 in its simplest radical form as follows:

√58812 = A√B

√58812 = 26√87

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