VTMO 2026 - Grade 7 - Semifinal - SET 3 - Self-study Question 9

Question 9

Let $a,b$ be arbitrary positive rational numbers. Which statement below is false?

1. $\dfrac{a}{\sqrt{b^4}}$ is rational.
2. $\dfrac{\sqrt{a^2}}b$ is rational.
3. $a^2-\sqrt{b^2}$ is rational.
4. $\sqrt{(-ab)^4}$ is rational.
5. $\sqrt{\dfrac{a^2b^4}{a^4b}}$ is rational.