To answer this question we will use the following examples:
1) Let a=b, then:
[tex]\sqrt{a*b}=\sqrt{a^2}=|a|.[/tex]
Since a is rational, then |a| is rational.
2) Let a=1 and b=2, then:
[tex]\sqrt{1*2}=\sqrt{2}.[/tex]
We know that √2 is an irrational number.
Therefore, if a and b are rational numbers, then:
[tex]\sqrt{ab}[/tex]
is sometimes a rational number.
Answer: Third option.
