Question

prove that (√3+√5) whole square

is an irrational number​

Answer 1

Let (√3+√5)be rational no

p/q= (√3+√5)

p^2/q^2= (√3)^2 + (√5)^2 +2×√3×√5

p^2/q^2=3+5+2√15

p^2/q^2=8+2√15

p^2/2q^2 - 4 = √15

since,p ,q,4and 2 are integers , so p^2/2q^2 - 4 is rational.

Therefore,√15is also rational

This contradict our supposition.