Question

prove that under root 2+under root 3 is irrational

Answer 1

let 2+√3 be a rational no.
therefore, 2 +√3= p/q (where p&q are co-prime)
                √3=p/q+3
                √3=p+3q/q
here, p is a integer; q is a integer and 3q is a integer
therefore, p+3q/q is a rational number
              but √3 is a irrational no.
              hence our supposition is wrong.
hence 2+√3 is a irrational number.

Answer 2

Let √2+√3= a (where 'a' is a rational no.)
a=√2+√3
a²=(√2+√3)² (squaring)
a²=2+3+2×√2×√3
a²=5+2√6
2√6=a²-5
√6=a²-5÷2
Since, a is rational number then a²-5÷2 is also a rational number but √6 is not rational so our assumption is wrong.
Hence,√2+√3 is irrational. PROVED