Simplify Square Root of 41971

Here we will show you two methods that you can use to simplify the square root of 41971. In other words, we will show you how to find the square root of 41971 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.

√41971 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 41971 to simplify the square root of 41971. 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 41971. The factors of 41971 are 1, 19, 47, 893, 2209, and 41971. Furthermore, the greatest perfect square on this list is 2209 and the square root of 2209 is 47. Therefore, A equals 47.

B = Calculate 41971 divided by the greatest perfect square from the list of all factors of 41971. We determined above that the greatest perfect square from the list of all factors of 41971 is 2209. Furthermore, 41971 divided by 2209 is 19, therefore B equals 19.

Now we have A and B and can get our answer to 41971 in its simplest radical form as follows:

√41971 = A√B

√41971 = 47√19

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 41971 to simplify the square root of 41971 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 41971 and then take the square root of that product. The prime factors that multiply together to make 41971 are 19 x 47 x 47. When we strip out the pairs only, we get 47 x 47 = 2209 and the square root of 2209 is 47. Therefore, A equals 47.

B = Divide 41971 by the number (A) squared. 47 squared is 2209 and 41971 divided by 2209 is 19. Therefore, B equals 19.

Once again we have A and B and can get our answer to 41971 in its simplest radical form as follows:

√41971 = A√B

√41971 = 47√19

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Simplify Square Root of 41972
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