Question

given that√5 is irrational prove that 3+7√5 is irrational number

Answer 1

here. the answer...
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Answer 2

let us assu3 + 7 under root 5 is a rational number me

so there exist co prime A and B such that

A/B= 3 + 7 root 5

A/B-3=7 root 5

3A-3/7B = root 5

as LHS is relational there polar RHS must be national

but it contradict the fact that root 5 is irrational this contradiction occur because of our wrong assumption that 3 + 7 root 5 is rational

Hans 3 + 7 root 5 is irrational number