Simplify Square Root of 2979

Here we will show you two methods that you can use to simplify the square root of 2979. In other words, we will show you how to find the square root of 2979 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.

√2979 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 2979 to simplify the square root of 2979. 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 2979. The factors of 2979 are 1, 3, 9, 331, 993, and 2979. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 2979 divided by the greatest perfect square from the list of all factors of 2979. We determined above that the greatest perfect square from the list of all factors of 2979 is 9. Furthermore, 2979 divided by 9 is 331, therefore B equals 331.

Now we have A and B and can get our answer to 2979 in its simplest radical form as follows:

√2979 = A√B

√2979 = 3√331

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 2979 to simplify the square root of 2979 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 2979 and then take the square root of that product. The prime factors that multiply together to make 2979 are 3 x 3 x 331. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 2979 by the number (A) squared. 3 squared is 9 and 2979 divided by 9 is 331. Therefore, B equals 331.

Once again we have A and B and can get our answer to 2979 in its simplest radical form as follows:

√2979 = A√B

√2979 = 3√331

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Simplify Square Root of 2980
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