Simplify Square Root of 66924

Here we will show you two methods that you can use to simplify the square root of 66924. In other words, we will show you how to find the square root of 66924 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.

√66924 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 66924 to simplify the square root of 66924. 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 66924. The factors of 66924 are 1, 2, 3, 4, 6, 9, 11, 12, 13, 18, 22, 26, 33, 36, 39, 44, 52, 66, 78, 99, 117, 132, 143, 156, 169, 198, 234, 286, 338, 396, 429, 468, 507, 572, 676, 858, 1014, 1287, 1521, 1716, 1859, 2028, 2574, 3042, 3718, 5148, 5577, 6084, 7436, 11154, 16731, 22308, 33462, and 66924. Furthermore, the greatest perfect square on this list is 6084 and the square root of 6084 is 78. Therefore, A equals 78.

B = Calculate 66924 divided by the greatest perfect square from the list of all factors of 66924. We determined above that the greatest perfect square from the list of all factors of 66924 is 6084. Furthermore, 66924 divided by 6084 is 11, therefore B equals 11.

Now we have A and B and can get our answer to 66924 in its simplest radical form as follows:

√66924 = A√B

√66924 = 78√11

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 66924 to simplify the square root of 66924 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 66924 and then take the square root of that product. The prime factors that multiply together to make 66924 are 2 x 2 x 3 x 3 x 11 x 13 x 13. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 13 x 13 = 6084 and the square root of 6084 is 78. Therefore, A equals 78.

B = Divide 66924 by the number (A) squared. 78 squared is 6084 and 66924 divided by 6084 is 11. Therefore, B equals 11.

Once again we have A and B and can get our answer to 66924 in its simplest radical form as follows:

√66924 = A√B

√66924 = 78√11

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