Question 1: Estimate the cube root of 50. Write your answer as a whole number or a simple fraction.

Answer: 3

Question 2: Estimate the cube root of 200. Show your working based on nearby perfect cubes.

Answer: 5.8

Question 3: Estimate the cube root of 730. Which two perfect cubes is this between?

Answer: 512 and 729

Question 4: Construct a rough estimate for the cube root of 1000 using the grid. Indicate your steps.

Answer: Since 1000 is a perfect cube of 10, the cube root is exactly 10.

Question 5: Estimate the cube root of 125, then verify by calculating the exact cube root.

Answer: 5

Question 6: A spherical ball has a volume of approximately 36π cubic units. Estimate its radius using cube root approximation.

Answer: Approximately 2 units

Question 7: Estimate the cube root of 10000. Which perfect cubes is this closest to?

Answer: 21.5 (between 216 and 1000)

Question 8: Identify and correct the mistake: The student estimates the cube root of 64 as 8 because 8³=512.

Answer: Mistake: 8³=512 is incorrect; 8³=512. The correct estimate should be 4, since 4³=64.

Question 9: Estimate the cube root of 1728 and compare it to the exact value.

Answer: Approximate estimate: 12; exact cube root: 12

Question 10: Challenge: Without precise calculation, estimate the cube root of 4104 and explain your reasoning.

Answer: Since 16³=4096, the cube root of 4104 is approximately 16.