Question

Explain why $\frac{\sqrt{3}}{2}$ is not a rational number.

Short answer

$\frac{\sqrt{3}}{2}$ is not a rational number because $\sqrt{3}$ is not an integer.

Step-by-step solution

- Define rational number.

The set of rational number has numbers in the ratio form $\frac{m}{n}$, where m and n are integers and n is non-zero. The decimal form of a rational number is either a terminating or repeating decimal

- Substitution in given values

Substitute m for $\sqrt{3}$and n for 2 in given term.

Now it becomes $\frac{m}{n}$

- Check 32 satisfies definition of rational number or not

For rational number in the form $\frac{m}{n}$, $m\text{and}n$are integers and n is non-zero.

Since, $\sqrt{3}$ is not an integer.

Thus, $\frac{\sqrt{3}}{2}$ is not a rational number.