Simplify Square Root of 73926

Here we will show you two methods that you can use to simplify the square root of 73926. In other words, we will show you how to find the square root of 73926 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.

√73926 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 73926 to simplify the square root of 73926. 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 73926. The factors of 73926 are 1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 111, 222, 333, 666, 999, 1369, 1998, 2738, 4107, 8214, 12321, 24642, 36963, and 73926. Furthermore, the greatest perfect square on this list is 12321 and the square root of 12321 is 111. Therefore, A equals 111.

B = Calculate 73926 divided by the greatest perfect square from the list of all factors of 73926. We determined above that the greatest perfect square from the list of all factors of 73926 is 12321. Furthermore, 73926 divided by 12321 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 73926 in its simplest radical form as follows:

√73926 = A√B

√73926 = 111√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 73926 to simplify the square root of 73926 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 73926 and then take the square root of that product. The prime factors that multiply together to make 73926 are 2 x 3 x 3 x 3 x 37 x 37. When we strip out the pairs only, we get 3 x 3 x 37 x 37 = 12321 and the square root of 12321 is 111. Therefore, A equals 111.

B = Divide 73926 by the number (A) squared. 111 squared is 12321 and 73926 divided by 12321 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 73926 in its simplest radical form as follows:

√73926 = A√B

√73926 = 111√6

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