Question 1: Simplify the expression 3/√5 by rationalising the denominator.

Answer: 3√5/5

Question 2: Rationalise the denominator of 7/√2.

Answer: 7√2/2

Question 3: Express 5/√3 in simplified form with rationalised denominator.

Answer: 5√3/3

Question 4: Calculate and simplify the expression: (2/√7) + (3/√7).

Answer: 5√7/7

Question 5: A telescope's lens has a focal length of 10/√2 meters. Rationalise the denominator of this length.

Answer: 10√2/2 meters

Question 6: An astronaut measures a distance of 4/√6 light-years. Rationalise the denominator to express the distance in simplest form.

Answer: 2√6 light-years

Question 7: Construct an expression similar to a/√b where a=9 and b=8. Simplify it after rationalising the denominator.

Answer: 9√8/8

Question 8: A satellite orbits at a distance of 15/√3 million kilometers from Earth. Rationalise the denominator for this distance.

Answer: 15√3/3 million kilometers

Question 9: Evaluate the expression: (6/√10) - (2/√10).

Answer: 4√10/10

Question 10: Identify and correct the mistake in simplifying 4/√6 to 4√6/6.

Answer: The mistake is that 4/√6 is not simplified; it should be rationalised to 4√6/6, which is correct.

Question 11: Simplify the expression (8/√2) and rationalise the denominator.

Answer: 8√2/2 = 4√2