a)
[tex]2+\sqrt{21}[/tex]
The result is irrational!
Because the sum of a rational and an irrational number is always irrational.
b)
[tex]\frac{10}{19}+\frac{5}{13}[/tex]
The result is rational!
The sum of two rational numbers is always rational. You can justify it by doing:
[tex]k=\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}\Rightarrow k\in\mathbb{Q}[/tex]
c)
[tex]\sqrt{14}\cdot18[/tex]
The result is irrational!
In fact, the product of an irrational and a rational will always be irrational.,
d)
[tex]15\cdot\frac{9}{16}[/tex]
The result is rational!
The product of two rational numbers is always rational
