Question 1: Simplify: √64 ÷ √16

Answer: 2

Question 2: Calculate √81 ÷ √9.

Answer: 3

Question 3: Express as a single surd: √50 ÷ √2.

Answer: 5

Question 4: If √a ÷ √b = 4, what is the value of √a if √b = 2?

Answer: 16

Question 5: Simplify: √18 ÷ √2.

Answer: 3

Question 6: A rectangle has a length of √200 meters and a width of √50 meters. Find the ratio of its length to width.

Answer: √200/√50 = √(200/50) = √4 = 2

Question 7: Calculate the value of √128 ÷ √8.

Answer: 4

Question 8: A garden design uses a circular lawn with radius √45 meters. A pathway surrounds the lawn at a radius of √20 meters. Find the ratio of the areas enclosed by the pathway and the lawn.

Answer: π(√20)^2 / π(√45)^2 = 20/45 = 4/9

Question 9: Simplify: √125 ÷ √5.

Answer: 5

Question 10: If √a ÷ √b = 3 and √a = 12, what is the value of √b?

Answer: 16

Question 11: Calculate: √72 ÷ √8.

Answer: 3

Question 12: Identify and correct the mistake in simplifying √45 ÷ √5 as 3.

Answer: Incorrect, √45 ÷ √5 = √(45/5) = √9 = 3 (correct). The mistake is assuming √45 ÷ √5 equals 3 without simplifying properly.