Simplify Square Root of 79461

Here we will show you two methods that you can use to simplify the square root of 79461. In other words, we will show you how to find the square root of 79461 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.

√79461 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 79461 to simplify the square root of 79461. 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 79461. The factors of 79461 are 1, 3, 9, 27, 81, 109, 243, 327, 729, 981, 2943, 8829, 26487, and 79461. Furthermore, the greatest perfect square on this list is 729 and the square root of 729 is 27. Therefore, A equals 27.

B = Calculate 79461 divided by the greatest perfect square from the list of all factors of 79461. We determined above that the greatest perfect square from the list of all factors of 79461 is 729. Furthermore, 79461 divided by 729 is 109, therefore B equals 109.

Now we have A and B and can get our answer to 79461 in its simplest radical form as follows:

√79461 = A√B

√79461 = 27√109

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 79461 to simplify the square root of 79461 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 79461 and then take the square root of that product. The prime factors that multiply together to make 79461 are 3 x 3 x 3 x 3 x 3 x 3 x 109. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 3 x 3 = 729 and the square root of 729 is 27. Therefore, A equals 27.

B = Divide 79461 by the number (A) squared. 27 squared is 729 and 79461 divided by 729 is 109. Therefore, B equals 109.

Once again we have A and B and can get our answer to 79461 in its simplest radical form as follows:

√79461 = A√B

√79461 = 27√109

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Simplify Square Root of 79462
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