Simplify Square Root of 69192

Here we will show you two methods that you can use to simplify the square root of 69192. In other words, we will show you how to find the square root of 69192 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.

√69192 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 69192 to simplify the square root of 69192. 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 69192. The factors of 69192 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 31, 36, 62, 72, 93, 124, 186, 248, 279, 372, 558, 744, 961, 1116, 1922, 2232, 2883, 3844, 5766, 7688, 8649, 11532, 17298, 23064, 34596, and 69192. Furthermore, the greatest perfect square on this list is 34596 and the square root of 34596 is 186. Therefore, A equals 186.

B = Calculate 69192 divided by the greatest perfect square from the list of all factors of 69192. We determined above that the greatest perfect square from the list of all factors of 69192 is 34596. Furthermore, 69192 divided by 34596 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 69192 in its simplest radical form as follows:

√69192 = A√B

√69192 = 186√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 69192 to simplify the square root of 69192 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 69192 and then take the square root of that product. The prime factors that multiply together to make 69192 are 2 x 2 x 2 x 3 x 3 x 31 x 31. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 31 x 31 = 34596 and the square root of 34596 is 186. Therefore, A equals 186.

B = Divide 69192 by the number (A) squared. 186 squared is 34596 and 69192 divided by 34596 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 69192 in its simplest radical form as follows:

√69192 = A√B

√69192 = 186√2

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