alleryWhich of the following is an irrational number?
A$0.\overline{27}$
B$\sqrt{2} + \sqrt{3}$
C$\dfrac{22}{7}$
D$\sqrt{16}$
Answer & Solution
Correct answer: B. $\sqrt{2} + \sqrt{3}$
$\sqrt{16}=4$ (rational), $0.\overline{27}$ is repeating (rational), $22/7$ is a fraction (rational).
$\sqrt2+\sqrt3$ is irrational — if it equalled a rational $r$, squaring gives $5 + 2\sqrt6 = r^2$, forcing $\sqrt6$ rational, a contradiction.
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