Simplify Square Root of 80828

Here we will show you two methods that you can use to simplify the square root of 80828. In other words, we will show you how to find the square root of 80828 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.

√80828 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 80828 to simplify the square root of 80828. 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 80828. The factors of 80828 are 1, 2, 4, 11, 22, 44, 121, 167, 242, 334, 484, 668, 1837, 3674, 7348, 20207, 40414, and 80828. Furthermore, the greatest perfect square on this list is 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Calculate 80828 divided by the greatest perfect square from the list of all factors of 80828. We determined above that the greatest perfect square from the list of all factors of 80828 is 484. Furthermore, 80828 divided by 484 is 167, therefore B equals 167.

Now we have A and B and can get our answer to 80828 in its simplest radical form as follows:

√80828 = A√B

√80828 = 22√167

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 80828 to simplify the square root of 80828 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 80828 and then take the square root of that product. The prime factors that multiply together to make 80828 are 2 x 2 x 11 x 11 x 167. When we strip out the pairs only, we get 2 x 2 x 11 x 11 = 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Divide 80828 by the number (A) squared. 22 squared is 484 and 80828 divided by 484 is 167. Therefore, B equals 167.

Once again we have A and B and can get our answer to 80828 in its simplest radical form as follows:

√80828 = A√B

√80828 = 22√167

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Simplify Square Root of 80829
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