Simplify Square Root of 79233

Here we will show you two methods that you can use to simplify the square root of 79233. In other words, we will show you how to find the square root of 79233 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.

√79233 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 79233 to simplify the square root of 79233. 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 79233. The factors of 79233 are 1, 3, 7, 11, 21, 33, 49, 77, 147, 231, 343, 539, 1029, 1617, 2401, 3773, 7203, 11319, 26411, and 79233. Furthermore, the greatest perfect square on this list is 2401 and the square root of 2401 is 49. Therefore, A equals 49.

B = Calculate 79233 divided by the greatest perfect square from the list of all factors of 79233. We determined above that the greatest perfect square from the list of all factors of 79233 is 2401. Furthermore, 79233 divided by 2401 is 33, therefore B equals 33.

Now we have A and B and can get our answer to 79233 in its simplest radical form as follows:

√79233 = A√B

√79233 = 49√33

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 79233 to simplify the square root of 79233 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 79233 and then take the square root of that product. The prime factors that multiply together to make 79233 are 3 x 7 x 7 x 7 x 7 x 11. When we strip out the pairs only, we get 7 x 7 x 7 x 7 = 2401 and the square root of 2401 is 49. Therefore, A equals 49.

B = Divide 79233 by the number (A) squared. 49 squared is 2401 and 79233 divided by 2401 is 33. Therefore, B equals 33.

Once again we have A and B and can get our answer to 79233 in its simplest radical form as follows:

√79233 = A√B

√79233 = 49√33

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Simplify Square Root of 79234
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