Simplify Square Root of 31914

Here we will show you two methods that you can use to simplify the square root of 31914. In other words, we will show you how to find the square root of 31914 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.

√31914 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 31914 to simplify the square root of 31914. 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 31914. The factors of 31914 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 197, 394, 591, 1182, 1773, 3546, 5319, 10638, 15957, and 31914. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 31914 divided by the greatest perfect square from the list of all factors of 31914. We determined above that the greatest perfect square from the list of all factors of 31914 is 81. Furthermore, 31914 divided by 81 is 394, therefore B equals 394.

Now we have A and B and can get our answer to 31914 in its simplest radical form as follows:

√31914 = A√B

√31914 = 9√394

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 31914 to simplify the square root of 31914 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 31914 and then take the square root of that product. The prime factors that multiply together to make 31914 are 2 x 3 x 3 x 3 x 3 x 197. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 31914 by the number (A) squared. 9 squared is 81 and 31914 divided by 81 is 394. Therefore, B equals 394.

Once again we have A and B and can get our answer to 31914 in its simplest radical form as follows:

√31914 = A√B

√31914 = 9√394

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Simplify Square Root of 31915
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