Question:
The smallest number by which $\sqrt{27}$ should be multiplied so as to get a rational number is
(a) $\sqrt{27}$
(b) $3 \sqrt{3}$
(c) $\sqrt{3}$
(d) 3
Solution:
$\sqrt{27}=\sqrt{3 \times 3 \times 3}$
$=3 \sqrt{3}$
Out of the given choices $\sqrt{3}$ is the only smallest number by which if we multiply $\sqrt{27}$ we get a rational number.
Hence, the correct choice is (c).