Simplify Square Root of 73008

Here we will show you two methods that you can use to simplify the square root of 73008. In other words, we will show you how to find the square root of 73008 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.

√73008 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 73008 to simplify the square root of 73008. 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 73008. The factors of 73008 are 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 27, 36, 39, 48, 52, 54, 72, 78, 104, 108, 117, 144, 156, 169, 208, 216, 234, 312, 338, 351, 432, 468, 507, 624, 676, 702, 936, 1014, 1352, 1404, 1521, 1872, 2028, 2704, 2808, 3042, 4056, 4563, 5616, 6084, 8112, 9126, 12168, 18252, 24336, 36504, and 73008. Furthermore, the greatest perfect square on this list is 24336 and the square root of 24336 is 156. Therefore, A equals 156.

B = Calculate 73008 divided by the greatest perfect square from the list of all factors of 73008. We determined above that the greatest perfect square from the list of all factors of 73008 is 24336. Furthermore, 73008 divided by 24336 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 73008 in its simplest radical form as follows:

√73008 = A√B

√73008 = 156√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 73008 to simplify the square root of 73008 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 73008 and then take the square root of that product. The prime factors that multiply together to make 73008 are 2 x 2 x 2 x 2 x 3 x 3 x 3 x 13 x 13. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 x 13 x 13 = 24336 and the square root of 24336 is 156. Therefore, A equals 156.

B = Divide 73008 by the number (A) squared. 156 squared is 24336 and 73008 divided by 24336 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 73008 in its simplest radical form as follows:

√73008 = A√B

√73008 = 156√3

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