Question

Classify the following number as rational or irrational with justification:

`sqrt(12)/sqrt(75)`

Answer 1

The given number is rational number.

Justification: `sqrt(12/17) = sqrt((3 xx 4)/(3 xx 25))`  ...(Simplifying the given expression)

= `sqrt(4/25)`  ...(Taking the square root)

= `2/5` 

Which is in form `p/q; q ≠ 0, p, q` both are integers.

Thus, `sqrt(12/75)` is rational.