Simplify Square Root of 79497

Here we will show you two methods that you can use to simplify the square root of 79497. In other words, we will show you how to find the square root of 79497 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.

√79497 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 79497 to simplify the square root of 79497. 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 79497. The factors of 79497 are 1, 3, 9, 11, 33, 73, 99, 121, 219, 363, 657, 803, 1089, 2409, 7227, 8833, 26499, and 79497. Furthermore, the greatest perfect square on this list is 1089 and the square root of 1089 is 33. Therefore, A equals 33.

B = Calculate 79497 divided by the greatest perfect square from the list of all factors of 79497. We determined above that the greatest perfect square from the list of all factors of 79497 is 1089. Furthermore, 79497 divided by 1089 is 73, therefore B equals 73.

Now we have A and B and can get our answer to 79497 in its simplest radical form as follows:

√79497 = A√B

√79497 = 33√73

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 79497 to simplify the square root of 79497 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 79497 and then take the square root of that product. The prime factors that multiply together to make 79497 are 3 x 3 x 11 x 11 x 73. When we strip out the pairs only, we get 3 x 3 x 11 x 11 = 1089 and the square root of 1089 is 33. Therefore, A equals 33.

B = Divide 79497 by the number (A) squared. 33 squared is 1089 and 79497 divided by 1089 is 73. Therefore, B equals 73.

Once again we have A and B and can get our answer to 79497 in its simplest radical form as follows:

√79497 = A√B

√79497 = 33√73

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Simplify Square Root of 79498
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