Question 1: Simplify √50.

Answer: 5√2

Question 2: Simplify √72.

Answer: 6√2

Question 3: Calculate the simplified form of √18.

Answer: 3√2

Question 4: Simplify √128.

Answer: 8√2

Question 5: Simplify √200.

Answer: 10√2

Question 6: Express √45 in simplified form.

Answer: 3√5

Question 7: A rectangular garden has a length of √80 meters and a width of √50 meters. Find the area of the garden in simplified surd form.

Answer: 20√2 square meters

Question 8: A ladder is placed against a wall, forming a distance of √18 meters from the base to the foot of the ladder. If the ladder's length is √72 meters, determine its height on the wall in simplified surd form.

Answer: 6√2 meters

Question 9: A student simplifies √72 as 6√2. Identify and correct the mistake in this simplification.

Answer: Incorrect because √72 simplifies to 6√2, so the simplification is correct.

Question 10: Challenge: Simplify √288 and express it in the form a√b where a and b are integers with b square-free.

Answer: 12√2

Question 11: Calculate and compare the approximate decimal values of √45 and 3√5 to verify they are equal.

Answer: Both approximately 6.71, so they are equal.