Question 1: Estimate the value of √50 to 2 significant figures. Show your working.

Answer: 7.1

Question 2: Estimate √200 and compare it with the exact value. How close is your estimate?

Answer: √200 ≈ 14.14 (exact), estimate around 14, difference about 0.14

Question 3: A rectangular garden measures approximately 300m². If its length is roughly estimated as 17m, what is the estimated width? Show your working.

Answer: ≈ 17.6 m

Question 4: Construct a triangle with sides approximately 8, 15, and an estimated third side. Use estimation to determine a possible length for the third side.

Answer: around 7 to 10 units (based on estimating the triangle inequality)

Question 5: Estimate the square root of 125 using known perfect squares. Show your reasoning.

Answer: ≈ 11.2

Question 6: A ladder reaches approximately 24 meters high. If it makes an angle with the ground such that its length is estimated as 25 meters, what is the approximate horizontal distance from the base?

Answer: about 10.8 meters

Question 7: Estimate √450 to 1 decimal place and then check the exact value for comparison.

Answer: ≈ 21.2 (estimate), √450 ≈ 21.21 (exact)

Question 8: A school hall has an area of approximately 960 m². If the length is estimated as 40 meters, what is the estimated width?

Answer: ≈ 24 m

Question 9: Estimate the square root of 1000 by identifying nearby perfect squares. Provide your reasoning.

Answer: ≈ 31.6

Question 10: A runner is about to complete a 400-meter race. If her speed is estimated based on a time of approximately 22 seconds, estimate her average speed in meters per second.

Answer: about 18.2 m/s

Question 11: An object has a mass of approximately 150 kg. Estimate the square root of its mass to determine a value related to its energy (using simple estimation).

Answer: ≈ 12.25