Let us assume that √3 + √5 is rational
On squaring, we get
(√3 + √5)2 is rational
3 + 2√3 x √5 + 5 is rational
8 + 2√15 is rational
Subtract 8 from above result, considering 8 is a rational number.
As we know, Difference of two rational numbers is a rational.
8 + 2√15 – 8 is rational
2√15 is rational
Which is only possible if 2 is rational and √15 is rational.
The fact is √15 is not a rational number.
Our assumption is wrong, and
(√3 + √5) is irrational.
