Simplify Square Root of 69984

Here we will show you two methods that you can use to simplify the square root of 69984. In other words, we will show you how to find the square root of 69984 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.

√69984 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 69984 to simplify the square root of 69984. 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 69984. The factors of 69984 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 243, 288, 324, 432, 486, 648, 729, 864, 972, 1296, 1458, 1944, 2187, 2592, 2916, 3888, 4374, 5832, 7776, 8748, 11664, 17496, 23328, 34992, and 69984. Furthermore, the greatest perfect square on this list is 11664 and the square root of 11664 is 108. Therefore, A equals 108.

B = Calculate 69984 divided by the greatest perfect square from the list of all factors of 69984. We determined above that the greatest perfect square from the list of all factors of 69984 is 11664. Furthermore, 69984 divided by 11664 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 69984 in its simplest radical form as follows:

√69984 = A√B

√69984 = 108√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 69984 to simplify the square root of 69984 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 69984 and then take the square root of that product. The prime factors that multiply together to make 69984 are 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 x 3. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 = 11664 and the square root of 11664 is 108. Therefore, A equals 108.

B = Divide 69984 by the number (A) squared. 108 squared is 11664 and 69984 divided by 11664 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 69984 in its simplest radical form as follows:

√69984 = A√B

√69984 = 108√6

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