June 2025 Paper 3 Q1

1 A student states that the product of two irrational numbers is always irrational.

One of the options is a counter example that shows the student’s statement is incorrect.

Identify the counter example.

Circle your answer. [1 mark]

• \(\mathrm{e} \times 0 = 0\)
• \(\dfrac{1}{\pi} \times \pi = 1\)
• \(\dfrac{1}{\sqrt{2}} \times \sqrt{6} = \sqrt{3}\)
• \(2 \times \sqrt{3} = \sqrt{6}\)