Simplify Square Root of 79623

Here we will show you two methods that you can use to simplify the square root of 79623. In other words, we will show you how to find the square root of 79623 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.

√79623 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 79623 to simplify the square root of 79623. 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 79623. The factors of 79623 are 1, 3, 9, 27, 81, 983, 2949, 8847, 26541, and 79623. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 79623 divided by the greatest perfect square from the list of all factors of 79623. We determined above that the greatest perfect square from the list of all factors of 79623 is 81. Furthermore, 79623 divided by 81 is 983, therefore B equals 983.

Now we have A and B and can get our answer to 79623 in its simplest radical form as follows:

√79623 = A√B

√79623 = 9√983

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 79623 to simplify the square root of 79623 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 79623 and then take the square root of that product. The prime factors that multiply together to make 79623 are 3 x 3 x 3 x 3 x 983. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 79623 by the number (A) squared. 9 squared is 81 and 79623 divided by 81 is 983. Therefore, B equals 983.

Once again we have A and B and can get our answer to 79623 in its simplest radical form as follows:

√79623 = A√B

√79623 = 9√983

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Simplify Square Root of 79624
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