Question 1: Simplify the expression 3/√2 by rationalising the denominator.

Answer: 3√2/2

Question 2: Rationalise the denominator of 5/√3.

Answer: 5√3/3

Question 3: Simplify (4/√5) and write the answer in the form a/√b.

Answer: 4√5/5

Question 4: Calculate and simplify the expression (7/√6).

Answer: 7√6/6

Question 5: Rationalise the denominator of 2/√7 and simplify your answer.

Answer: 2√7/7

Question 6: Simplify (9/√2) in the form a/√b.

Answer: 9√2/2

Question 7: Construct an expression in the form a/√b that is equivalent to (12/√3).

Answer: 12√3/3

Question 8: Explain why rationalising the denominator is necessary when working with expressions like 4/√5.

Answer: Rationalising removes the square root from the denominator, making the expression easier to interpret, compare, and work with in calculations.

Question 9: Simplify (6/√8) and write the answer in simplest form.

Answer: 6√8/8 = 3√2/4

Question 10: A box contains (10/√2) meters of fabric. Rationalise the denominator and find the total length in meters.

Answer: 10√2/2 = 5√2 meters

Question 11: Evaluate and rationalise (8/√3) and write your answer in simplest form.

Answer: 8√3/3