Simplify Square Root of 36166

Here we will show you two methods that you can use to simplify the square root of 36166. In other words, we will show you how to find the square root of 36166 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.

√36166 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 36166 to simplify the square root of 36166. 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 36166. The factors of 36166 are 1, 2, 13, 26, 107, 169, 214, 338, 1391, 2782, 18083, and 36166. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 36166 divided by the greatest perfect square from the list of all factors of 36166. We determined above that the greatest perfect square from the list of all factors of 36166 is 169. Furthermore, 36166 divided by 169 is 214, therefore B equals 214.

Now we have A and B and can get our answer to 36166 in its simplest radical form as follows:

√36166 = A√B

√36166 = 13√214

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 36166 to simplify the square root of 36166 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 36166 and then take the square root of that product. The prime factors that multiply together to make 36166 are 2 x 13 x 13 x 107. When we strip out the pairs only, we get 13 x 13 = 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Divide 36166 by the number (A) squared. 13 squared is 169 and 36166 divided by 169 is 214. Therefore, B equals 214.

Once again we have A and B and can get our answer to 36166 in its simplest radical form as follows:

√36166 = A√B

√36166 = 13√214

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Simplify Square Root of 36167
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