Simplify Square Root of 79092

Here we will show you two methods that you can use to simplify the square root of 79092. In other words, we will show you how to find the square root of 79092 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.

√79092 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 79092 to simplify the square root of 79092. 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 79092. The factors of 79092 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 169, 234, 338, 468, 507, 676, 1014, 1521, 2028, 2197, 3042, 4394, 6084, 6591, 8788, 13182, 19773, 26364, 39546, and 79092. Furthermore, the greatest perfect square on this list is 6084 and the square root of 6084 is 78. Therefore, A equals 78.

B = Calculate 79092 divided by the greatest perfect square from the list of all factors of 79092. We determined above that the greatest perfect square from the list of all factors of 79092 is 6084. Furthermore, 79092 divided by 6084 is 13, therefore B equals 13.

Now we have A and B and can get our answer to 79092 in its simplest radical form as follows:

√79092 = A√B

√79092 = 78√13

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 79092 to simplify the square root of 79092 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 79092 and then take the square root of that product. The prime factors that multiply together to make 79092 are 2 x 2 x 3 x 3 x 13 x 13 x 13. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 13 x 13 = 6084 and the square root of 6084 is 78. Therefore, A equals 78.

B = Divide 79092 by the number (A) squared. 78 squared is 6084 and 79092 divided by 6084 is 13. Therefore, B equals 13.

Once again we have A and B and can get our answer to 79092 in its simplest radical form as follows:

√79092 = A√B

√79092 = 78√13

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