Question 1: Simplify √50 and express your answer in simplest radical form.

Answer: 5√2

Question 2: Calculate the value of √81 and √32. Show your working.

Answer: 9 and 4√2

Question 3: Simplify √200 and express your answer with a single radical.

Answer: 10√2

Question 4: Construct a triangle on the grid with sides of length √8, √18, and √50. Label the sides with their simplified radical forms.

Answer: Student constructs triangle with sides labeled as 2√2, 3√2, and 5√2

Question 5: Simplify √72 and √200, then compare which is larger.

Answer: 6√2 and 10√2; 10√2 is larger

Question 6: A square garden has an area of 200 m². Find the length of one side in simplest radical form.

Answer: 10√2 meters

Question 7: Simplify √18 + √50. Show your working and express your answer in simplest radical form.

Answer: 3√2 + 5√2 = 8√2

Question 8: Identify and correct the mistake: Simplify √75 as 5√3 and √12 as 2√3, then add them to get 7√3.

Answer: Error: √75 simplifies to 5√3, but √12 simplifies to 2√3. Their sum is 7√3, which is correct. The mistake is in assuming the sum of radicals is straightforward addition—it's only valid if the radicals are the same.

Question 9: Challenge: Simplify √180 without a calculator, and express your answer in simplest radical form.

Answer: 6√5

Question 10: A rectangular piece of cloth measures √8 meters by √32 meters. Find the area in simplest radical form.

Answer: 4√2 × 4√2 = 16×2 = 32 m²

Question 11: Express √150 in simplest radical form. Then, estimate its approximate value.

Answer: 5√6 and approximately 12.2

Question 12: Explain why √48 can be simplified to 4√3, and identify a common mistake when simplifying √n.

Answer: √48 = √16×3 = 4√3 because 16 is a perfect square. Common mistake: simplifying √48 to 8√3, which is incorrect.