Question 1: Calculate the exact value of √49.

Answer: 7

Question 2: Calculate √81 and explain why it is equal to 9, not -9.

Answer: √81 = 9 because square roots denote the principal (non-negative) root.

Question 3: Identify the mistake in the following statement: '√36 = -6'.

Answer: The mistake is that √36 = 6, not -6; square roots are defined as non-negative.

Question 4: Estimate the value of √50 and justify your answer.

Answer: Approximately 7.07 because √49=7 and √64=8, so √50 is slightly more than 7.

Question 5: Simplify √144 and explain your process.

Answer: √144=12 because 144 is a perfect square: 12×12=144.

Question 6: A ball is dropped from a height of 16 meters. How long does it take to hit the ground if its height is proportional to the square of time? Use √16 in your reasoning.

Answer: It takes 4 units of time because height = k×(time)^2, so √16=4; with proportionality, time = √height = 4.

Question 7: Construct a square with side length √25 on the grid. Describe the steps.

Answer: Plot a line of length 5 units (since √25=5) on the grid and form a square using this length.

Question 8: A student claims that √36 = ±6. Is this correct? Justify your answer.

Answer: The claim is partially correct; √36 = 6 as the principal root. The symbol ±6 indicates both roots, but √36 specifically denotes 6.

Question 9: Find the exact value of √(25×4) and explain the property used.

Answer: √(25×4)=√25×√4=5×2=10; using √a×b=√a×√b.

Question 10: Identify the error: Student calculates √64 as 8 and then claims √(64/4)=8. Correct the mistake.

Answer: The mistake is that √(64/4)=√64/√4=8/2=4, not 8.

Question 11: Challenge: Express √18 in simplest form and justify why no further simplification is possible.

Answer: √18=√(9×2)=√9×√2=3√2; cannot simplify further because 2 is not a perfect square.