Answer:

Consider,

√3 + √5 be rational.

∴√3 + √5 = a, where a is rational.

∴ √3 = a – √5

Square on both sides,

3 = (a – √5)

2 = a

2 + 5 – 2√5a

This is impossible because right-hand side is rational, whereas the left-hand side is irrational.

This is a contradiction.

Thus, √3 + √5 is irrational.