Question 1: Calculate the value of √16 × √25.

Answer: 20

Question 2: Simplify √9 × √4.

Answer: 6

Question 3: Calculate √36 × √49.

Answer: 42

Question 4: If √a × √b = √(a×b), what is √64 × √81?

Answer: 72

Question 5: Evaluate √100 × √9.

Answer: 30

Question 6: A student incorrectly thinks that √a × √b = √(a + b). Identify and correct their mistake when they try to simplify √25 × √16.

Answer: They should multiply under the radical: √(25×16) = √400 = 20. Their mistake was adding instead of multiplying.

Question 7: Complete the calculation: √49 × √25 = ____.

Answer: 35

Question 8: Identify the common misconception: Why is √36 × √49 ≠ √(36 + 49)?

Answer: Because √a × √b = √(a×b), not √(a + b).

Question 9: Calculate √81 × √64.

Answer: 72

Question 10: A misconception is that √a × √b always simplifies to √(a + b). Provide an example where this misconception leads to an incorrect answer and explain the correct process.

Answer: For example, √16 × √25 ≠ √(16 + 25). Correct way: √(16×25) = √400 = 20.

Question 11: Express √36 × √49 as a simplified surd, then as a decimal.

Answer: √36 × √49 = √(36×49) = √1764 = 42, decimal: 42

Question 12: Challenge: Simplify √a × √b where a=121 and b=144, then verify your answer by multiplication.

Answer: √121 × √144 = √(121×144) = √17424 ≈ 132, verification: 11×12=132