Question

Prove that (√3 +√5 )² is an irrational no.

Answer 1

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Answer 2

let us assume that (√3+√5)^2 be a rational number

(√3+√5)^2=a/b (where a and b are coprime numbers and b is not equal to 0)

3+2√15+5=a/b

8+2√15=a/b

2√15=a/b-8

2√15=a-8b/b

√15=a-8b/2b

√15 is an irrational number and the rhs is a rational number therefore lhs is not equal to rhs.

therefore our assumption was wrong.

(√3+√5)^2 is an irrational number

Hence proved.