Simplify Square Root of 27828

Here we will show you two methods that you can use to simplify the square root of 27828. In other words, we will show you how to find the square root of 27828 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.

√27828 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 27828 to simplify the square root of 27828. 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 27828. The factors of 27828 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 773, 1546, 2319, 3092, 4638, 6957, 9276, 13914, and 27828. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 27828 divided by the greatest perfect square from the list of all factors of 27828. We determined above that the greatest perfect square from the list of all factors of 27828 is 36. Furthermore, 27828 divided by 36 is 773, therefore B equals 773.

Now we have A and B and can get our answer to 27828 in its simplest radical form as follows:

√27828 = A√B

√27828 = 6√773

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 27828 to simplify the square root of 27828 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 27828 and then take the square root of that product. The prime factors that multiply together to make 27828 are 2 x 2 x 3 x 3 x 773. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 27828 by the number (A) squared. 6 squared is 36 and 27828 divided by 36 is 773. Therefore, B equals 773.

Once again we have A and B and can get our answer to 27828 in its simplest radical form as follows:

√27828 = A√B

√27828 = 6√773

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Simplify Square Root of 27829
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