Question 1: Calculate the simplified form of √18 × √8.

Answer: √144 = 12

Question 2: Evaluate √50 × √2.

Answer: √100 = 10

Question 3: Simplify √32 × √18.

Answer: √576 = 24

Question 4: Calculate √200 × √50.

Answer: √10000 = 100

Question 1: A construction worker needs to calculate the length of a diagonal across a square garden with side length √12 meters. What is the length of the diagonal?

Answer: Diagonal = √(12×2) = √24 ≈ 4.90 meters

Question 2: A piece of fabric measures √45 meters in length. If a designer cuts sections each measuring √5 meters, how many sections can be cut?

Answer: Number of sections = √45 ÷ √5 = √(45/5) = √9 = 3

Question 3: A rectangular pool has dimensions √20 meters by √80 meters. Find the area of the pool.

Answer: Area = √20 × √80 = √(20×80) = √1600 = 40 square meters

Question 1: A builder is installing tiles in a square pattern. Each tile covers an area of √2 square meters. If the total area to be covered is √50 square meters, how many tiles are needed?

Answer: Number of tiles = √50 ÷ √2 = √(50/2) = √25 = 5 tiles

Question 2: An engineer is designing a ramp with a length of √72 meters and height √8 meters. What is the slope of the ramp?

Answer: Slope = √8 ÷ √72 = √(8/72) = √(1/9) = 1/3

Question 1: Simplify the expression √50 × √18 ÷ √2.

Answer: √(50×18/2) = √(900) = 30

Question 2: If √a × √b = 10 and √a = 2√3, find the value of √b.

Answer: √a = 2√3 → a = (2√3)^2 = 4×3 = 12; then √a × √b = 10 → √12 × √b = 10 → √b = 10 / √12 = 10 / (2√3) = (10/2)×(√3/√3) = 5√3/3

Question 1: Construct a triangle with sides of √3, √12, and √15 on the grid above.

Answer: Students draw the triangle accordingly.

Question 2: Plot the graph of y=2x for x values of √1, √4, and √9.

Answer: Points (√1, 2×√1), (√4, 2×√4), (√9, 2×√9).

Question 3: Identify the common mistake when simplifying √50 × √8 as √400 instead of √(50×8).

Answer: Students often incorrectly assume √a × √b = √(a + b) instead of √(a×b).