Simplify Square Root of 41327

Here we will show you two methods that you can use to simplify the square root of 41327. In other words, we will show you how to find the square root of 41327 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.

√41327 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 41327 to simplify the square root of 41327. 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 41327. The factors of 41327 are 1, 11, 13, 17, 143, 187, 221, 289, 2431, 3179, 3757, and 41327. Furthermore, the greatest perfect square on this list is 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Calculate 41327 divided by the greatest perfect square from the list of all factors of 41327. We determined above that the greatest perfect square from the list of all factors of 41327 is 289. Furthermore, 41327 divided by 289 is 143, therefore B equals 143.

Now we have A and B and can get our answer to 41327 in its simplest radical form as follows:

√41327 = A√B

√41327 = 17√143

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 41327 to simplify the square root of 41327 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 41327 and then take the square root of that product. The prime factors that multiply together to make 41327 are 11 x 13 x 17 x 17. When we strip out the pairs only, we get 17 x 17 = 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Divide 41327 by the number (A) squared. 17 squared is 289 and 41327 divided by 289 is 143. Therefore, B equals 143.

Once again we have A and B and can get our answer to 41327 in its simplest radical form as follows:

√41327 = A√B

√41327 = 17√143

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Simplify Square Root of 41328
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