Question 1: Estimate √50 by identifying the perfect squares closest to 50.

Answer: 7.1

Question 2: Estimate √200 using perfect squares.

Answer: 14.1

Question 3: Calculate a rough estimate of √125.

Answer: 11.2

Question 1: A square has an area of 300 cm². Estimate the length of one side and explain your method.

Answer: Approximately 17.3 cm, by noting that √300 is between √289=17 and √324=18, closer to 17.3.

Question 2: A rectangle's diagonal measures approximately √50 units. Estimate the lengths of its sides, assuming they are equal. Show your working.

Answer: About 5.4 units for each side, since the sides are roughly √(50/2)=√25+√25=5+5=10, so sides are around 5.4 each.

Question 1: A car travels a distance of approximately √180 miles. Estimate the distance traveled and explain your reasoning.

Answer: Approximately 13.4 miles, since √180 is between √169=13 and √196=14, closer to 13.4.

Question 2: A bookshelf has an estimated height of √500 cm. What is the estimated height? Show your working.

Answer: About 22.4 cm, as √500 is between √484=22 and √529=23, closer to 22.4.

Question 1: Estimate √750 with reasoning, then compare your estimate to the actual value. Discuss possible sources of error in your estimation.

Answer: Estimate about 27.4, since √729=27 and √784=28, closer to 27.4. Errors may arise from approximating the distance between perfect squares.

Question 2: Construct a diagram on the grid showing the estimation of √32 by marking the approximate position between √25 and √36.

Answer: Plot between 5 and 6, closer to 5.7.

Question 1: A student estimates √80 as 9. Is this correct? Explain why or why not, and correct the mistake if necessary.

Answer: Incorrect; √80 is approximately 8.9, so estimating as 9 is close but slightly over. The mistake is assuming it's exactly 9. Refer to perfect squares 81 and 64.

Question 2: A student incorrectly estimates √200 as 15. Identify the mistake and provide the correct estimate.

Answer: Incorrect; √200 is about 14.1, so estimating as 15 slightly overestimates. The mistake is assuming √200 is close to 15 instead of recognizing it's closer to 14.1.