The product of which of the following is a rational number? 

Concept -

Definition: A rational number is any number that can be expressed as a fraction of two integers, where the denominator (the bottom part of the fraction) is not zero.

Form: A rational number can be written in the form p/q​, where p and
q are integers and q ≠ 0 and gcd(p, q ) = 1 

√a × √b = √ab

Explanation -

For option (i) -

√2 × √3 = √2 x 3 = √6

It does not give a rational number

For option (ii) -

√9 × √5= √9 x 5 = √45

It does not give a rational number

For option (iii) -

√27 × √3= √27 x 3 = √81 = 9 

It gives a rational number

Hence option (3) is correct.