Simplify Square Root of 40344

Here we will show you two methods that you can use to simplify the square root of 40344. In other words, we will show you how to find the square root of 40344 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.

√40344 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 40344 to simplify the square root of 40344. 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 40344. The factors of 40344 are 1, 2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492, 984, 1681, 3362, 5043, 6724, 10086, 13448, 20172, and 40344. Furthermore, the greatest perfect square on this list is 6724 and the square root of 6724 is 82. Therefore, A equals 82.

B = Calculate 40344 divided by the greatest perfect square from the list of all factors of 40344. We determined above that the greatest perfect square from the list of all factors of 40344 is 6724. Furthermore, 40344 divided by 6724 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 40344 in its simplest radical form as follows:

√40344 = A√B

√40344 = 82√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 40344 to simplify the square root of 40344 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 40344 and then take the square root of that product. The prime factors that multiply together to make 40344 are 2 x 2 x 2 x 3 x 41 x 41. When we strip out the pairs only, we get 2 x 2 x 41 x 41 = 6724 and the square root of 6724 is 82. Therefore, A equals 82.

B = Divide 40344 by the number (A) squared. 82 squared is 6724 and 40344 divided by 6724 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 40344 in its simplest radical form as follows:

√40344 = A√B

√40344 = 82√6

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Simplify Square Root of 40345
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