Question

Prove that 7+√2 is irrational

Answer 1

Hey mate here is ur ans
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@heeny.....

Hope it helps u

Answer 2

${ hey \: mate \: here \: is \: your \: answer}$
$let \: 7 + \sqrt{2}$

is as rational.
$7 + \sqrt{2 \ \: } = \frac{a}{b} \: \: \: \:$

(where b is not equal to 0)
where a,b are co prime .
$\frac{a}{b} - 7 = \sqrt{2 }$
$so \: by \: lcm \: on \: lhs \: \\ we \: get$
$\frac{a - 7b}{b}$
and now a and b are integers so it will be rational.
and so _/2 is a rational number .But this contradict the fact that _/2 is an irrational number.
so , our hypothesis is wrong.
so,we can conclude that 7+_/2 is an irrational number