Simplify Square Root of 27708

Here we will show you two methods that you can use to simplify the square root of 27708. In other words, we will show you how to find the square root of 27708 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.

√27708 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 27708 to simplify the square root of 27708. 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 27708. The factors of 27708 are 1, 2, 3, 4, 6, 12, 2309, 4618, 6927, 9236, 13854, and 27708. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 27708 divided by the greatest perfect square from the list of all factors of 27708. We determined above that the greatest perfect square from the list of all factors of 27708 is 4. Furthermore, 27708 divided by 4 is 6927, therefore B equals 6927.

Now we have A and B and can get our answer to 27708 in its simplest radical form as follows:

√27708 = A√B

√27708 = 2√6927

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 27708 to simplify the square root of 27708 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 27708 and then take the square root of that product. The prime factors that multiply together to make 27708 are 2 x 2 x 3 x 2309. 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 27708 by the number (A) squared. 2 squared is 4 and 27708 divided by 4 is 6927. Therefore, B equals 6927.

Once again we have A and B and can get our answer to 27708 in its simplest radical form as follows:

√27708 = A√B

√27708 = 2√6927

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Simplify Square Root of 27709
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