Simplify Square Root of 98022

Here we will show you two methods that you can use to simplify the square root of 98022. In other words, we will show you how to find the square root of 98022 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.

√98022 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 98022 to simplify the square root of 98022. 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 98022. The factors of 98022 are 1, 2, 3, 6, 17, 31, 34, 51, 62, 93, 102, 186, 527, 961, 1054, 1581, 1922, 2883, 3162, 5766, 16337, 32674, 49011, and 98022. Furthermore, the greatest perfect square on this list is 961 and the square root of 961 is 31. Therefore, A equals 31.

B = Calculate 98022 divided by the greatest perfect square from the list of all factors of 98022. We determined above that the greatest perfect square from the list of all factors of 98022 is 961. Furthermore, 98022 divided by 961 is 102, therefore B equals 102.

Now we have A and B and can get our answer to 98022 in its simplest radical form as follows:

√98022 = A√B

√98022 = 31√102

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 98022 to simplify the square root of 98022 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 98022 and then take the square root of that product. The prime factors that multiply together to make 98022 are 2 x 3 x 17 x 31 x 31. When we strip out the pairs only, we get 31 x 31 = 961 and the square root of 961 is 31. Therefore, A equals 31.

B = Divide 98022 by the number (A) squared. 31 squared is 961 and 98022 divided by 961 is 102. Therefore, B equals 102.

Once again we have A and B and can get our answer to 98022 in its simplest radical form as follows:

√98022 = A√B

√98022 = 31√102

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Simplify Square Root of 98023
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