
Here we will show you two methods that you can use to simplify the square root of 33282. In other words, we will show you how to find the square root of 33282 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.
√33282 = A√B
Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 33282 to simplify the square root of 33282. 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 33282. The factors of 33282 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, 774, 1849, 3698, 5547, 11094, 16641, and 33282. Furthermore, the greatest perfect square on this list is 16641 and the square root of 16641 is 129. Therefore, A equals 129.
B = Calculate 33282 divided by the greatest perfect square from the list of all factors of 33282. We determined above that the greatest perfect square from the list of all factors of 33282 is 16641. Furthermore, 33282 divided by 16641 is 2, therefore B equals 2.
Now we have A and B and can get our answer to 33282 in its simplest radical form as follows:
√33282 = A√B
√33282 = 129√2
Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 33282 to simplify the square root of 33282 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 33282 and then take the square root of that product. The prime factors that multiply together to make 33282 are 2 x 3 x 3 x 43 x 43. When we strip out the pairs only, we get 3 x 3 x 43 x 43 = 16641 and the square root of 16641 is 129. Therefore, A equals 129.
B = Divide 33282 by the number (A) squared. 129 squared is 16641 and 33282 divided by 16641 is 2. Therefore, B equals 2.
Once again we have A and B and can get our answer to 33282 in its simplest radical form as follows:
√33282 = A√B
√33282 = 129√2
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