Question

Classify the following number as rational or irrational with justification:

`sqrt(9/27)`

Answer 1

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.