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

Answer: 20

Question 2: Simplify √9 × √49.

Answer: 21

Question 3: Calculate √36 × √64.

Answer: 48

Question 4: Explain why √a × √b = √(a×b) is valid for positive a and b.

Answer: Because the square root function is multiplicative over positive numbers, so √a × √b = √(a×b).

Question 5: Calculate √18 × √2 using properties of surds.

Answer: 6

Question 6: If √a × √b = 12 and √a = 3, find the value of √b.

Answer: 16

Question 7: Construct and simplify the expression √50 × √8.

Answer: 20√2

Question 8: A garden has a rectangular area with length √80 meters and width √20 meters. Find the total area in simplest surd form.

Answer: 20√2 m²

Question 9: Calculate √12 × √75 and simplify your answer.

Answer: 30

Question 10: A construction project requires tiles with side length √18 meters. If the total area required is √72 square meters, how many tiles are needed? (Express in simplest surd form).

Answer: 2√2 tiles

Question 11: Identify and correct the mistake: Simplify √50 × √2 as 10.

Answer: Incorrect, because √50 × √2 = √(50×2) = √100 = 10. The mistake was in the initial simplification step.