Final answer:
To estimate 796 × 6.05² + 4.1 using approximations to 1 significant figure, we round relevant numbers and calculate 800 × 40 to get an estimated result of 32,000.
Step-by-step explanation:
To estimate the value of 796 × 6.05² + 4.1 using approximations to 1 significant figure, we first round off the numbers to one significant figure: 796 becomes 800 and 6.05 becomes 6. Squaring 6 gives us 36. So, we now estimate 800 × 36 + 4 which rounds to 800 × 40 because 36 rounds to one significant figure as 40. Therefore, the estimated calculation is 800 × 40 = 32,000. We then add the 4.1, which is insignificant in this context, giving us an estimated result of 32,000. Remember, we are working to one significant figure, so our final result should reflect this level of precision.