Simplify Square Root of 40068

Here we will show you two methods that you can use to simplify the square root of 40068. In other words, we will show you how to find the square root of 40068 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.

√40068 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 40068 to simplify the square root of 40068. 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 40068. The factors of 40068 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 53, 54, 63, 84, 106, 108, 126, 159, 189, 212, 252, 318, 371, 378, 477, 636, 742, 756, 954, 1113, 1431, 1484, 1908, 2226, 2862, 3339, 4452, 5724, 6678, 10017, 13356, 20034, and 40068. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 40068 divided by the greatest perfect square from the list of all factors of 40068. We determined above that the greatest perfect square from the list of all factors of 40068 is 36. Furthermore, 40068 divided by 36 is 1113, therefore B equals 1113.

Now we have A and B and can get our answer to 40068 in its simplest radical form as follows:

√40068 = A√B

√40068 = 6√1113

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 40068 to simplify the square root of 40068 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 40068 and then take the square root of that product. The prime factors that multiply together to make 40068 are 2 x 2 x 3 x 3 x 3 x 7 x 53. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 40068 by the number (A) squared. 6 squared is 36 and 40068 divided by 36 is 1113. Therefore, B equals 1113.

Once again we have A and B and can get our answer to 40068 in its simplest radical form as follows:

√40068 = A√B

√40068 = 6√1113

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