Question

Subtraction of a rational number and an irrational number gives always.

• A. a rational number
• B. an irrational number
• C. zero

Answer 1

The correct option is B an irrational number

Eg.
5 is a rational number and $\sqrt{3}$ is an irrational number.
Subtraction of these two numbers give 5-$\sqrt{3}$.
Lets assume 5-$\sqrt{3}$ is a rational number.
5-$\sqrt{3}$ = $\frac{a}{b}$, $b\ne 0$
$⟹$ 5 - $\frac{a}{b}$ = $\sqrt{3}$
$⟹$ $\frac{5b-a}{b}$ = $\sqrt{3}$
But, $\frac{5b-a}{b}$ is a rational number and $\sqrt{3}$ is an irrational number.
Thus, there is a contradiction to our assumption that 5-$\sqrt{3}$ is a rational number.
Hence, 5-$\sqrt{3}$ is an irrational number.
Similarly, 5+$\sqrt{3}$ is also an irrational number.