Question

prove 3√7 is an irrational number

Answer 1

let 3√7 be rational
hence , 3√7 = a/b

√7 = a/3b
since, irrational does not equal to rational
hence , our assumption is wrong .
hence , 3√7 is irrational

Answer 2

$\huge \bf \red{ \mid{ \overline{ \underline{ANSWER}}} \mid}$

Let 3√7 be a rational number

Hence

→ 3√7 = a/b where a and b are integers and b≠ 0

$\bf \implies 3 \sqrt{7} = \frac{a}{b} \\ \\ \bf \implies \sqrt{7} = \frac{a}{3b}$

» Here a/3b is a rational number , but √7 is an irrational number .

Hence the contadiction we supposed is wrong !

» hence 3√7 is an irrational number