Question 1: Simplify the expression: √144 ÷ √16.

Answer: 3

Question 2: Calculate √81 ÷ √9 and explain your process.

Answer: 3

Question 3: If √a ÷ √b = √(a/b), find the value of a and b given that the quotient is 5, where a = 25b.

Answer: a=125, b=25

Question 4: Identify and correct the mistake in simplifying √36 ÷ √4 as 6 ÷ 2 = 3.

Answer: Incorrect; should be √(36/4) = √9 = 3

Question 5: Evaluate √50 ÷ √2 using the property √a ÷ √b = √(a/b).

Answer: 5

Question 6: Construct an expression involving √a ÷ √b where the simplified result is √3.

Answer: √12 ÷ √4

Question 7: Solve for a and b: √a ÷ √b = √(a/b) = 4, with a = 3b.

Answer: a=48, b=12

Question 8: A student simplifies √81 ÷ √25 as 9 ÷ 5. Is this correct? Explain.

Answer: Yes, correct; √81 ÷ √25 = √(81/25) = √(3^4/5^2) = 3/5

Question 9: Express √a ÷ √b in terms of a single square root when a = 50 and b = 2.

Answer: √(50/2) = √25 = 5

Question 10: Calculate and verify: √200 ÷ √8 = √(200/8). Is the simplified answer correct?

Answer: √25 = 5

Question 11: A graph shows the function y = √(x). Plot the point corresponding to x = 16.

Answer: (16,4)

Question 12: Construct a surd expression involving √a ÷ √b where the division results in √3, with a and b positive integers.

Answer: √27 ÷ √9