Question

Use a calculator to evaluate the expression. Round the results to the nearest hundredth. $$\frac{6 \pm 4 \sqrt{2}}{-1}$$

Short answer

The rounded expressions for \(\frac{6 \pm 4 \sqrt{2}}{-1}\) are -9.66 when using plus operation and -2.34 when using the minus operation.

Step-by-step solution

Simplify the expression with a plus operation

First, find the positive root of 2, then multiply it by 4, add the result to 6, and divide by -1. This can be written as: \(-(6+4 \sqrt{2})\)

Simplify the expression with a minus operation

For the second calculation, take the positive root of 2, multiply it by 4, subtract the result from 6, and divide by -1. This gives \(-(6-4 \sqrt{2})\)

Round both results to the nearest hundredth

Now, take both results from steps 1 and 2 and round to the nearest hundredth. This would involve getting at least two decimal places, dropping the third decimal place, and rounding up or down as applicable