Simplify Square Root of 27840

Here we will show you two methods that you can use to simplify the square root of 27840. In other words, we will show you how to find the square root of 27840 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.

√27840 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 27840 to simplify the square root of 27840. 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 27840. The factors of 27840 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 29, 30, 32, 40, 48, 58, 60, 64, 80, 87, 96, 116, 120, 145, 160, 174, 192, 232, 240, 290, 320, 348, 435, 464, 480, 580, 696, 870, 928, 960, 1160, 1392, 1740, 1856, 2320, 2784, 3480, 4640, 5568, 6960, 9280, 13920, and 27840. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 27840 divided by the greatest perfect square from the list of all factors of 27840. We determined above that the greatest perfect square from the list of all factors of 27840 is 64. Furthermore, 27840 divided by 64 is 435, therefore B equals 435.

Now we have A and B and can get our answer to 27840 in its simplest radical form as follows:

√27840 = A√B

√27840 = 8√435

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 27840 to simplify the square root of 27840 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 27840 and then take the square root of that product. The prime factors that multiply together to make 27840 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 29. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 27840 by the number (A) squared. 8 squared is 64 and 27840 divided by 64 is 435. Therefore, B equals 435.

Once again we have A and B and can get our answer to 27840 in its simplest radical form as follows:

√27840 = A√B

√27840 = 8√435

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Simplify Square Root of 27841
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