Question

prove that 3+√5,1/√2 6+√2 and 5-√3 is irrational

Answer 1

Now i am telling a simple trick . The addition, subtraction , multiplication and division of rational and irrational is always irrational.

Answer 2

A - Let 3 + √5 be a rational number
.°. 3 + √5 = p/q [ where p and q are integer , q ≠ 0 and q and p are co - prime number ]
=> √5 = p/q - 3
=> √5 = p - 3q/q
we know that p/q is a rational number.
.°. √5 is also a rational number.
This contradicts our assumption.
.°. 3 +√5 is an irrational number.