Simplify Square Root of 27735

Here we will show you two methods that you can use to simplify the square root of 27735. In other words, we will show you how to find the square root of 27735 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.

√27735 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 27735 to simplify the square root of 27735. 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 27735. The factors of 27735 are 1, 3, 5, 15, 43, 129, 215, 645, 1849, 5547, 9245, and 27735. Furthermore, the greatest perfect square on this list is 1849 and the square root of 1849 is 43. Therefore, A equals 43.

B = Calculate 27735 divided by the greatest perfect square from the list of all factors of 27735. We determined above that the greatest perfect square from the list of all factors of 27735 is 1849. Furthermore, 27735 divided by 1849 is 15, therefore B equals 15.

Now we have A and B and can get our answer to 27735 in its simplest radical form as follows:

√27735 = A√B

√27735 = 43√15

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 27735 to simplify the square root of 27735 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 27735 and then take the square root of that product. The prime factors that multiply together to make 27735 are 3 x 5 x 43 x 43. When we strip out the pairs only, we get 43 x 43 = 1849 and the square root of 1849 is 43. Therefore, A equals 43.

B = Divide 27735 by the number (A) squared. 43 squared is 1849 and 27735 divided by 1849 is 15. Therefore, B equals 15.

Once again we have A and B and can get our answer to 27735 in its simplest radical form as follows:

√27735 = A√B

√27735 = 43√15

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Simplify Square Root of 27736
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