Simplify Square Root of 80832

Here we will show you two methods that you can use to simplify the square root of 80832. In other words, we will show you how to find the square root of 80832 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.

√80832 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 80832 to simplify the square root of 80832. 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 80832. The factors of 80832 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 421, 842, 1263, 1684, 2526, 3368, 5052, 6736, 10104, 13472, 20208, 26944, 40416, and 80832. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 80832 divided by the greatest perfect square from the list of all factors of 80832. We determined above that the greatest perfect square from the list of all factors of 80832 is 64. Furthermore, 80832 divided by 64 is 1263, therefore B equals 1263.

Now we have A and B and can get our answer to 80832 in its simplest radical form as follows:

√80832 = A√B

√80832 = 8√1263

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 80832 to simplify the square root of 80832 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 80832 and then take the square root of that product. The prime factors that multiply together to make 80832 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 421. 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 80832 by the number (A) squared. 8 squared is 64 and 80832 divided by 64 is 1263. Therefore, B equals 1263.

Once again we have A and B and can get our answer to 80832 in its simplest radical form as follows:

√80832 = A√B

√80832 = 8√1263

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Simplify Square Root of 80833
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