Examine whether the following number is rational or irrational:
$- \sqrt{81}$

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Solution

Simplify the given expression
$- \sqrt{81} =$ $- \sqrt{9 \times 9} = - 9$
Since, rational numbers are the numbers which can be written in $\frac{p}{q}$ form, where $p, q$ are integers and $q$ is not equal to zero.
$- 9$ can also be written in $\frac{p}{q}$ form as $- \frac{9}{1}$ .
Hence $- \sqrt{81}$ is a rational number.

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