Lovellss

2022-06-19

If ${c}^{2}=12$, then show that c is an irrational number.

### Answer & Explanation

Paxton James

$\begin{array}{rl}{x}^{2}& =3\\ {\left(\frac{c}{2}\right)}^{2}& =3\\ \frac{{c}^{2}}{4}& =3\\ {c}^{2}& =12\\ c& =±2\sqrt{3}\end{array}$
Since $\sqrt{3}$ is irrational, so is $±2\sqrt{3}$

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