Prove that √2+√3 is irrational. [3 MARKS]
Concept : 1 Mark
Application : 2 Marks
Let √2+√3 be rational number say 'x'
⇒x=√2+√3
x2=2+3+2√6
⇒x2=5+2√6
⇒√6=x2−52
As x, 5 and 2 are rationals,
⇒x2−52 is a rational number.
⇒√6=x2−52 is a rational number
which is contradiction to the fact that √6 is an irrational number.
Hence our assumption is wrong.
⇒√2+√3 is an irrational number.