Question

Prove that 3√10is an irrational number.​

Answer 1

$\star$ $\large\underline\mathrm\red{To \: prove :-}$ $3\sqrt{10} \: is \: an \: irrational \: number.$

$\large\underline\mathrm\red{Proof :-}$

$Let \: us \: assume \: 3\sqrt{10} \:as \: a \: rational \: number.$

Rational number are in the form of $\frac {p}{q} or$ $\frac {a}{b}$

$= 3\sqrt{10} = \frac {a}{b}$

$= \sqrt{10} = \frac {a}{3b}$

$\quad$ Our assumption or contradiction that 3√10 is wrong, therefore 3√10 is an irrational number.

•°• Hence proved.