Final answer:
To determine which inequalities are true, you must calculate the square roots, perform basic arithmetic, and compare the results using approximate values for irrational numbers like π.
Step-by-step explanation:
The question asks to evaluate which of the given inequalities are true. To solve each inequality, we will need to perform calculations and compare the expressions on each side using approximate values for irrational numbers, such as π (pi), which is approximately 3.14159. Let's analyze each option provided:
- A. √14 + 6.2 < 3π - 8.2: First, approximate the square root of 14 and add it to 6.2. Then calculate 3 times π, and subtract 8.2 from it. Compare the results to see if the inequality holds.
- B. 17/5 + √64 > 8 + π: Convert 17/5 to a decimal, and add the square root of 64 to it. Next, add 8 to π. Compare the results to check the validity of the inequality.
- C. 35 - √40 > 6π: Subtract the square root of 40 from 35. Then multiply 6 times π. Finally, compare the two results to conclude if the inequality is true or false.
The above approach will help in determining the correctness of each inequality statement. Remember to use approximate values when working with irrational numbers.