Question 1: Calculate the value of √16 × √9.

Answer: 12

Question 2: Simplify √25 × √4.

Answer: 10

Question 3: Express √18 × √50 as a simplified surd.

Answer: 3√200

Question 4: Calculate √12 × √75 and simplify your answer.

Answer: 30

Question 5: A square garden has side lengths of √8 meters and √18 meters. Find the area of the garden.

Answer: 144

Question 6: Simplify √50 × √2 and express your answer as a simplified surd.

Answer: 10

Question 7: Evaluate √81 × √x if x=16.

Answer: 36

Question 8: If √a × √b = √(a×b), what is the value of √7 × √3?

Answer: √21

Question 9: Identify the mistake: A student claims √50 × √2 = √100 and gives the answer 10. Is this correct? Explain your reasoning.

Answer: No, because √50 × √2 = √(50×2) = √100, which is correct, but the student should write √100, not 10.

Question 10: Challenge: Simplify √200 × √8 and express your answer as a simplified surd.

Answer: 4√50

Question 11: Construct a product of surds that equals √12 × √75 and show the simplified form.

Answer: √12 × √75 = √(12×75) = √900 = 30