Question

prove that (✓3+✓5)² is irrational number.​

Answer 1

Answer:

let assume to the contrary, that (√3+√5)² is a rational number

therefore, (√3+√5)²=a/b (where,a&b are co primes)

now, 3+√30+5=a/b

or 8+√30=a/b

√30=a/b-8

since a &b are co primes and a/b-8b/b is a rational number so √30is also rational

but the fact is that √30 is irrational

therefore, we can say that (√3+√5)² is irrational