Question

Evaluate the expression to the nearest hundredth. $$ \frac{2 \pm 6 \sqrt{3}}{3} $$

Short answer

The two results are approximately 4.13 and -2.80

Step-by-step solution

Calculate positive square root

Calculate \(6 \sqrt{3}\) which means multiply 6 by the square root of 3. By using a calculator, you find that it equals approximately 10.39.

Perform Addition and Subtraction Separately

Now, we perform the addition and subtraction operations separately, which gives us two results: (2 + 10.39) and (2 - 10.39). The result of these two operations will be approximately 12.39 and -8.39 respectively.

Divide by 3

For the final step, divide both results of step 2 by 3. The first result (12.39) divided by 3 is approximately 4.13; the second result (-8.39) divided by 3 is approximately -2.80.