Simplify Square Root of 96832

Here we will show you two methods that you can use to simplify the square root of 96832. In other words, we will show you how to find the square root of 96832 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.

√96832 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 96832 to simplify the square root of 96832. 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 96832. The factors of 96832 are 1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 89, 136, 178, 272, 356, 544, 712, 1088, 1424, 1513, 2848, 3026, 5696, 6052, 12104, 24208, 48416, and 96832. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 96832 divided by the greatest perfect square from the list of all factors of 96832. We determined above that the greatest perfect square from the list of all factors of 96832 is 64. Furthermore, 96832 divided by 64 is 1513, therefore B equals 1513.

Now we have A and B and can get our answer to 96832 in its simplest radical form as follows:

√96832 = A√B

√96832 = 8√1513

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 96832 to simplify the square root of 96832 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 96832 and then take the square root of that product. The prime factors that multiply together to make 96832 are 2 x 2 x 2 x 2 x 2 x 2 x 17 x 89. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 96832 by the number (A) squared. 8 squared is 64 and 96832 divided by 64 is 1513. Therefore, B equals 1513.

Once again we have A and B and can get our answer to 96832 in its simplest radical form as follows:

√96832 = A√B

√96832 = 8√1513

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