Question

prove root 3 + root 5 is irrational

Answer 1

Solution:-

given by:-

Ans:- Let √3+√5 be a rational number.

A rational number can be written in the form of p/q where p,q are integers.

=>√3+√5 = p/q

=>√3 = p/q-√5

Squaring on both sides,

=>(√3)² = (p/q-√5)²

=>3 = p²/q²+√5²-2(p/q)(√5)

=>√5×2p/q = p²/q²+5-3

=> √5 = (p²+2q²)/q² × q/2p

=>√5 = (p²+2q²)/2pq

p,q are integers then (p²+2q²)/2pq is a rational number. Then √5 is also a rational number.

But this contradicts the fact that √5 is an irrational number. So,our supposition is false.

Therefore, √3+√5 is an irrational number. (Ans)


☆i hope its help☆

Answer 2

root5 is irrational no.Addition with irrational no. is also irrational .So,3+root5 is irrational