Simplify Square Root of 31939

Here we will show you two methods that you can use to simplify the square root of 31939. In other words, we will show you how to find the square root of 31939 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.

√31939 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 31939 to simplify the square root of 31939. 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 31939. The factors of 31939 are 1, 19, 41, 779, 1681, and 31939. Furthermore, the greatest perfect square on this list is 1681 and the square root of 1681 is 41. Therefore, A equals 41.

B = Calculate 31939 divided by the greatest perfect square from the list of all factors of 31939. We determined above that the greatest perfect square from the list of all factors of 31939 is 1681. Furthermore, 31939 divided by 1681 is 19, therefore B equals 19.

Now we have A and B and can get our answer to 31939 in its simplest radical form as follows:

√31939 = A√B

√31939 = 41√19

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 31939 to simplify the square root of 31939 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 31939 and then take the square root of that product. The prime factors that multiply together to make 31939 are 19 x 41 x 41. When we strip out the pairs only, we get 41 x 41 = 1681 and the square root of 1681 is 41. Therefore, A equals 41.

B = Divide 31939 by the number (A) squared. 41 squared is 1681 and 31939 divided by 1681 is 19. Therefore, B equals 19.

Once again we have A and B and can get our answer to 31939 in its simplest radical form as follows:

√31939 = A√B

√31939 = 41√19

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Simplify Square Root of 31940
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