Question 1: Simplify: √50 ÷ √2

Answer: 5

Question 2: Calculate the value of √72 ÷ √8.

Answer: 3

Question 3: Express as a simplified surd: √200 ÷ √50.

Answer: 2

Question 4: Construct a division of surds where √a ÷ √b results in √(a/b) with a being 81 and b being 9. Write the simplified surd.

Answer: 3

Question 5: If √x ÷ √y = 4, and y = 9, find the value of x.

Answer: 144

Question 6: A student simplifies √180 ÷ √12. Show each step and find the answer.

Answer: 3

Question 7: In a real-world context, a garden has √98 meters of fencing on one side and √32 meters on the adjacent side. Find the total length of fencing needed if these are divided and added together.

Answer: 10

Question 8: Construct a problem where dividing √a by √b gives √(a/b), with specific values a=144 and b=36, and ask to verify the result.

Answer: 2

Question 9: A calculator shows √243 ÷ √3. Without using a calculator, simplify this expression and explain your steps.

Answer: 3√27

Question 10: Identify and correct the mistake in this student's work: √50 ÷ √8 = √(50/8) = √(6.25) = 2.5. Explain the error and provide the correct answer.

Answer: Incorrect simplification; √(50/8) = √(25/4) = 5/2 = 2.5, which is correct, so the mistake is in the initial step of simplification not shown properly.