Question

which of the following is rational number ​

Answer 1

Note: the given question is incomplete as it should be as follows:

which of the following is rational number?

a) $\sqrt{3}$     b) $4-6i$   c) $2$   d) $7i$

Solution:

Know that, a rational number is a number that can be expressed in the form of $\frac{p}{q}$, where $q\neq 0$.

Check option (a).

Observe that the given number is of the form $\sqrt{3}$.

Understand that this cannot be expressed in the form of  of $\frac{p}{q}$, where $q\neq 0$.

Therefore, the number $\sqrt{3}$ is not a rational number.

Check option (b).

Observe that the given number is of the form $4-6i$ .  

Understand that this cannot be expressed in the form of  of $\frac{p}{q}$, where $q\neq 0$ as it has iota in it which is an imaginary number.

Therefore, the number $4-6i$    is not a rational number.

Check option (c).

Observe that the given number is of the form $2$.

$2=\frac{2}{1}$

Understand that this can be expressed in the form of  of $\frac{p}{q}$, where $q\neq 0$.

Therefore, the number $2$ is a rational number.

Check option (d).

Observe that the given number is of the form $7i$ .  

Understand that this cannot be expressed in the form of  of $\frac{p}{q}$, where $q\neq 0$ as it has iota in it which is an imaginary number.

Therefore, the number $7i$   is not a rational number.