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Which of the following is an irrational number?

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\sqrt{\frac{8}{18}}

\sqrt{\frac{12}{3}}

\sqrt{\frac{28}{8}}

\sqrt{81}

answer is C.

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Detailed Solution

Given numbers are,

\sqrt{\frac{8}{18}}

\sqrt{\frac{12}{3}}

\sqrt{\frac{28}{8}}

and

\sqrt{81}

.
Rational numbers are numbers that are expressed as fractions. They can be positive, negative or zero. Rational numbers are of the form

\frac{p}{q}

, where q≠0. Rational numbers can be non-terminating and repeating.
Option (1)

:

\sqrt{\frac{8}{18}} = \sqrt{\frac{4}{9}}

\Rightarrow \frac{2}{3}

Hence, it is rational.
Option (2)

:

\sqrt{\frac{12}{3}} = \sqrt{4}

\Rightarrow 2

Hence, it is a rational number.
Option (3):

\sqrt{\frac{28}{8}} = \sqrt{\frac{7}{2}}

This cannot be simplified further. This is an irrational number.
Option (4)

:

\sqrt{81} = 9

This is a rational number.
Thus, only

\sqrt{\frac{28}{8}}

is an irrational number.
Therefore, option (3) is correct.

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