Simplify Square Root of 30984

Here we will show you two methods that you can use to simplify the square root of 30984. In other words, we will show you how to find the square root of 30984 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.

√30984 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 30984 to simplify the square root of 30984. 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 30984. The factors of 30984 are 1, 2, 3, 4, 6, 8, 12, 24, 1291, 2582, 3873, 5164, 7746, 10328, 15492, and 30984. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 30984 divided by the greatest perfect square from the list of all factors of 30984. We determined above that the greatest perfect square from the list of all factors of 30984 is 4. Furthermore, 30984 divided by 4 is 7746, therefore B equals 7746.

Now we have A and B and can get our answer to 30984 in its simplest radical form as follows:

√30984 = A√B

√30984 = 2√7746

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 30984 to simplify the square root of 30984 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 30984 and then take the square root of that product. The prime factors that multiply together to make 30984 are 2 x 2 x 2 x 3 x 1291. 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 30984 by the number (A) squared. 2 squared is 4 and 30984 divided by 4 is 7746. Therefore, B equals 7746.

Once again we have A and B and can get our answer to 30984 in its simplest radical form as follows:

√30984 = A√B

√30984 = 2√7746

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Simplify Square Root of 30985
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