Simplify Square Root of 27636

Here we will show you two methods that you can use to simplify the square root of 27636. In other words, we will show you how to find the square root of 27636 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.

√27636 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 27636 to simplify the square root of 27636. 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 27636. The factors of 27636 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 47, 49, 84, 94, 98, 141, 147, 188, 196, 282, 294, 329, 564, 588, 658, 987, 1316, 1974, 2303, 3948, 4606, 6909, 9212, 13818, and 27636. Furthermore, the greatest perfect square on this list is 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Calculate 27636 divided by the greatest perfect square from the list of all factors of 27636. We determined above that the greatest perfect square from the list of all factors of 27636 is 196. Furthermore, 27636 divided by 196 is 141, therefore B equals 141.

Now we have A and B and can get our answer to 27636 in its simplest radical form as follows:

√27636 = A√B

√27636 = 14√141

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 27636 to simplify the square root of 27636 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 27636 and then take the square root of that product. The prime factors that multiply together to make 27636 are 2 x 2 x 3 x 7 x 7 x 47. When we strip out the pairs only, we get 2 x 2 x 7 x 7 = 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Divide 27636 by the number (A) squared. 14 squared is 196 and 27636 divided by 196 is 141. Therefore, B equals 141.

Once again we have A and B and can get our answer to 27636 in its simplest radical form as follows:

√27636 = A√B

√27636 = 14√141

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