Simplify Square Root of 41323

Here we will show you two methods that you can use to simplify the square root of 41323. In other words, we will show you how to find the square root of 41323 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.

√41323 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 41323 to simplify the square root of 41323. 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 41323. The factors of 41323 are 1, 31, 43, 961, 1333, and 41323. Furthermore, the greatest perfect square on this list is 961 and the square root of 961 is 31. Therefore, A equals 31.

B = Calculate 41323 divided by the greatest perfect square from the list of all factors of 41323. We determined above that the greatest perfect square from the list of all factors of 41323 is 961. Furthermore, 41323 divided by 961 is 43, therefore B equals 43.

Now we have A and B and can get our answer to 41323 in its simplest radical form as follows:

√41323 = A√B

√41323 = 31√43

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 41323 to simplify the square root of 41323 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 41323 and then take the square root of that product. The prime factors that multiply together to make 41323 are 31 x 31 x 43. When we strip out the pairs only, we get 31 x 31 = 961 and the square root of 961 is 31. Therefore, A equals 31.

B = Divide 41323 by the number (A) squared. 31 squared is 961 and 41323 divided by 961 is 43. Therefore, B equals 43.

Once again we have A and B and can get our answer to 41323 in its simplest radical form as follows:

√41323 = A√B

√41323 = 31√43

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Simplify Square Root of 41324
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