Question

prove that root2+root7 is an irrational ​

Answer 1

assume that root2+root7 is rational

√2+√7=p/q

squaring on both sides

(√2+√7)^2=(p/q)^2

√2^2+√7^2+2(√2)(√7)=p^2/q^2

2+2+2√14=p^2/q^2

4+2√14=p^2/q^2

2√14=p^2-4q^2/q^2

√14=p^2-4q^2/2q^2

Rhs side Al are rational no then √14is also rational

but this contradicts the fact that root 14 in irrational

therefore root2+root7 is irrational