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Question
Classify the following number as rational or irrational with justification:
`sqrt(9/27)`
Solution
The given number is irrational number.
Justification: `sqrt(9/27) = sqrt(1/3)` ...(Simplifying the given expression)
= `1/sqrt(3)`
= `1/sqrt(3) xx sqrt(3)/sqrt(3)`
= `sqrt(3)/3`
Which is product of a rational number `(1/3)` and an irrational number `(sqrt(3))`, which results in an irrational number.
Thus, `sqrt(9/27)` is irrational.
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