Which of the following best explains why $\sqrt{3}$ is irrational?

Question

Accepted Answer

B. Because assuming $\sqrt{3}=\frac{a}{b}$ in lowest terms forces both $a$ and $b$ to be divisible by 3

Assume $\sqrt{3}=\frac{a}{b}$ with $a$ and $b$ coprime. Then $3b^2=a^2$, so 3 divides $a^2$, hence 3 divides $a$. Substituting $a=3c$ gives $b^2=3c^2$, so 3 divides $b$ too. This contradicts $a$ and $b$ being coprime, so $\sqrt{3}$ is irrational.

Answer

Because 3 is not a natural number

Answer

Because $\sqrt{3}$ has a terminating decimal expansion

Answer

Because every square root is irrational