Question

Prove the √5is irrational number hence show that 3+√5 is also irrational

Answer 1

root5 has no common factor so assume that root5is rational and p/q has no common factir

root5=p/q

squaring on both sides

(root5)²=(p/q)²

5=p²/q²

5q²=p²

so 5 is a factor of p²

also 5 is a factor of p

let p=5m

5q²=(5m)²

5q²=25m²

q²=5m²

so 5 is a factor of q²

also 5 is a factor of q

Hence we said that root5 is rational but according to our contradiction root5is irrational.

3+root5=k

root5 =k-3

LHS is irrational we know that and also RHS is irrational so 3+root5 is irrational

Answer 2

Step-by-step explanation:

HERE is your answer☝️☝️