Simplify Square Root of 40414

Here we will show you two methods that you can use to simplify the square root of 40414. In other words, we will show you how to find the square root of 40414 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.

√40414 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 40414 to simplify the square root of 40414. 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 40414. The factors of 40414 are 1, 2, 11, 22, 121, 167, 242, 334, 1837, 3674, 20207, and 40414. Furthermore, the greatest perfect square on this list is 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Calculate 40414 divided by the greatest perfect square from the list of all factors of 40414. We determined above that the greatest perfect square from the list of all factors of 40414 is 121. Furthermore, 40414 divided by 121 is 334, therefore B equals 334.

Now we have A and B and can get our answer to 40414 in its simplest radical form as follows:

√40414 = A√B

√40414 = 11√334

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 40414 to simplify the square root of 40414 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 40414 and then take the square root of that product. The prime factors that multiply together to make 40414 are 2 x 11 x 11 x 167. When we strip out the pairs only, we get 11 x 11 = 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Divide 40414 by the number (A) squared. 11 squared is 121 and 40414 divided by 121 is 334. Therefore, B equals 334.

Once again we have A and B and can get our answer to 40414 in its simplest radical form as follows:

√40414 = A√B

√40414 = 11√334

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Simplify Square Root of 40415
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