Question

prove that √5 + 3√5 is an irrational number​

Answer 1

Answer:

let us assume the contrary that √5+3√5 is rational then ,√5+3√5=a/b √5+√5=a/3b (squaring both sides) (√5+√5)^2=(a/3b)^2 √5^2+√5^2+2√5×√5=a^2/9b^2 5+5+2×5=a^2/9b^2 20 = a^2/9b^2 20/1=a^2/9b^2 both are rational numbers but we know that √5+3√5 is irrational and irrational is not equal to rational number so,our contradiction is arisen because of our incorrect assumption that√5+3√5 is rational number Hence ,√5+3√5 is an irrational number proved.