Simplify Square Root of 83232

Here we will show you two methods that you can use to simplify the square root of 83232. In other words, we will show you how to find the square root of 83232 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.

√83232 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 83232 to simplify the square root of 83232. 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 83232. The factors of 83232 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 32, 34, 36, 48, 51, 68, 72, 96, 102, 136, 144, 153, 204, 272, 288, 289, 306, 408, 544, 578, 612, 816, 867, 1156, 1224, 1632, 1734, 2312, 2448, 2601, 3468, 4624, 4896, 5202, 6936, 9248, 10404, 13872, 20808, 27744, 41616, and 83232. Furthermore, the greatest perfect square on this list is 41616 and the square root of 41616 is 204. Therefore, A equals 204.

B = Calculate 83232 divided by the greatest perfect square from the list of all factors of 83232. We determined above that the greatest perfect square from the list of all factors of 83232 is 41616. Furthermore, 83232 divided by 41616 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 83232 in its simplest radical form as follows:

√83232 = A√B

√83232 = 204√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 83232 to simplify the square root of 83232 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 83232 and then take the square root of that product. The prime factors that multiply together to make 83232 are 2 x 2 x 2 x 2 x 2 x 3 x 3 x 17 x 17. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 x 17 x 17 = 41616 and the square root of 41616 is 204. Therefore, A equals 204.

B = Divide 83232 by the number (A) squared. 204 squared is 41616 and 83232 divided by 41616 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 83232 in its simplest radical form as follows:

√83232 = A√B

√83232 = 204√2

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