Simplify Square Root of 82744

Here we will show you two methods that you can use to simplify the square root of 82744. In other words, we will show you how to find the square root of 82744 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.

√82744 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 82744 to simplify the square root of 82744. 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 82744. The factors of 82744 are 1, 2, 4, 8, 10343, 20686, 41372, and 82744. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 82744 divided by the greatest perfect square from the list of all factors of 82744. We determined above that the greatest perfect square from the list of all factors of 82744 is 4. Furthermore, 82744 divided by 4 is 20686, therefore B equals 20686.

Now we have A and B and can get our answer to 82744 in its simplest radical form as follows:

√82744 = A√B

√82744 = 2√20686

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 82744 to simplify the square root of 82744 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 82744 and then take the square root of that product. The prime factors that multiply together to make 82744 are 2 x 2 x 2 x 10343. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 82744 by the number (A) squared. 2 squared is 4 and 82744 divided by 4 is 20686. Therefore, B equals 20686.

Once again we have A and B and can get our answer to 82744 in its simplest radical form as follows:

√82744 = A√B

√82744 = 2√20686

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Simplify Square Root of 82745
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