Lesson 14: Surds and Operations [PATHS]

Year 10 Mathematics Unit 1 — Block B | Worksheet



Multiple Choice

Q1. Simplify sqrt(50).

A) 5sqrt(2) B) 2sqrt(5) C) 25sqrt(2) D) 10sqrt(5)

Q2. Simplify 3sqrt(5) + 2sqrt(5).

A) 5sqrt(10) B) 6sqrt(5) C) 5sqrt(5) D) 5sqrt(25)

Q3. Rationalise 2 / sqrt(3).

A) 2sqrt(3)/3 B) sqrt(3)/2 C) 2/3 D) 2sqrt(3)

Q4. Which is NOT equal to sqrt(12)?

A) 2sqrt(3) B) sqrt(4) x sqrt(3) C) 3sqrt(2) D) sqrt(24) / sqrt(2)

Q5. A square has area 18 cm^2. What is the exact side length?

A) 3sqrt(2) cm B) 9sqrt(2) cm C) 2sqrt(3) cm D) 4.24 cm

Short Answer

Q6. Simplify sqrt(72) + sqrt(50). (2 marks)

Q7. Rationalise 5 / sqrt(5) and simplify your answer fully. (3 marks)

Q8. Explain why mathematicians prefer to leave answers in exact surd form rather than using decimal approximations. Use sqrt(2) as an example. (3 marks)

Key Formulas