Question:
Which of the following is irrational?
(a) $\sqrt{\frac{4}{9}}$
(b) $\frac{\sqrt{12}}{\sqrt{3}}$
(c) $\sqrt{7}$
(d) $\sqrt{81}$
Solution:
(c)
$\sqrt{\frac{4}{9}}=\frac{2}{3}$ (rational)
$\frac{\sqrt{12}}{\sqrt{3}}=\frac{2 \sqrt{3}}{\sqrt{3}}=2$ (rational)
$\sqrt{81}=9$ (rational)
but $\sqrt{7}$ is an irrational number.
Hence, $\sqrt{7}$ is an irrational number.
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