Question

If root 3 is irrational, Prove that 2+5 root3 is an irrational number.

Answer 1

2 and 5 are rational and multiplying a rational no. to a irrational no. gives an irrational no. and 2(rational)+5 root 3 (irrational as explained above) give a irrational no. adding a rational to an irrational no. gives an irrational no.