Q2. - Algebra 2

Question

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

Step-by-Step Solution

Answer

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

Step 1 - 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

Step 2 - Substitution in given values

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

Now it becomes $\frac{m}{n}$ 

Step 3 - Check 3 2 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.