Question 1: Simplify √49 ÷ √7.

Answer: √49 ÷ √7 = 7 ÷ √7 = √7

Question 2: Evaluate √16 ÷ √4.

Answer: √16 ÷ √4 = 4 ÷ 2 = 2

Question 3: Calculate √81 ÷ √3.

Answer: √81 ÷ √3 = 9 ÷ √3 = 3√3

Question 1: Simplify √(25) ÷ √(5).

Answer: √25 ÷ √5 = 5 ÷ √5 = √5

Question 2: Express √(36) ÷ √(9) in simplest form.

Answer: √36 ÷ √9 = 6 ÷ 3 = 2

Question 3: If √a ÷ √b = 2 and a = 16, find b.

Answer: √16 ÷ √b = 2 ⇒ 4 ÷ √b = 2 ⇒ √b = 2 ⇒ b = 4

Question 4: Simplify the expression √(49) ÷ √(x), where x = 7.

Answer: √49 ÷ √7 = 7 ÷ √7 = √7

Question 1: Simplify √(a^2 * b) ÷ √(a * c), expressing your answer in terms of a, b, and c.

Answer: √(a^2 * b) ÷ √(a * c) = (a√b) ÷ √(a c) = (a√b) / (√a * √c) = (a√b) / (√a * √c) = (a / √a) * (√b / √c) = √a * (√b / √c)

Question 2: If √(x) ÷ √(y) = 3 and x = 25, find y.

Answer: √25 ÷ √y = 3 ⇒ 5 ÷ √y = 3 ⇒ √y = 5/3 ⇒ y = (5/3)^2 = 25/9

Question 3: Identify and correct the mistake in simplifying √(36) ÷ √(b) = √(36/b), when b = 49.

Answer: Incorrect, because √(36) ÷ √(b) ≠ √(36/b) unless both are positive. When b = 49, √(36) ÷ √(49) = 6 ÷ 7.