Question 1: Estimate the square root of 50. Round your answer to the nearest whole number.

Answer: 7

Question 2: Calculate the approximate value of √18. Show your working.

Answer: 4.2

Question 3: Estimate the square root of 200 and explain your reasoning.

Answer: The square root of 200 is approximately 14, since 14^2=196 and 15^2=225, so √200 is closer to 14.

Question 4: Construct a triangle with side lengths approximately √45, √80, and √30. Use the grid to sketch and label the sides.

Answer: Sides approximately 6.7, 8.9, and 5.5 respectively.

Question 5: Estimate √125 and √300. Show your working steps.

Answer: √125 ≈ 11, √300 ≈ 17

Question 6: A rectangle has an area of approximately 150 square units, with one side about √50. Estimate the length of the other side.

Answer: Approximately 3 units, since area ≈ 150 and one side ≈ 7, so the other side ≈ 150/7 ≈ 21.4, which is not consistent—so re-evaluate: the side about √50 ≈ 7, thus other side ≈ 150/7 ≈ 21.4.

Question 7: Estimate the square root of 625. Verify your estimate.

Answer: 25

Question 8: A box has a volume of about 3000 cubic units. If its length is roughly √120, estimate its width if the height is about √25.

Answer: Length ≈ 11, height ≈ 5, so width ≈ 3000/(11×5) ≈ 3000/55 ≈ 54.5 units.

Question 9: Estimate √50 and √32. Which is greater? Justify your answer.

Answer: √50 ≈ 7, √32 ≈ 5.7, so √50 is greater because 7 > 5.7.

Question 10: Estimate the value of √405. Show your working and compare it to the exact value.

Answer: √405 ≈ 20.1, since 20^2=400 and 21^2=441, so √405 is about 20.1.

Question 11: Identify and correct the mistake: Estimating √70 gives 9 because 9×9=81, which is greater than 70.

Answer: The mistake is estimating √70 as 9; since 8^2=64 and 9^2=81, √70 is closer to 8.4.