Question

(1) prove that √13+√17 is an irrational number.
(2)can two numbers have 18 as their HCF and 380 as their LCM. give reason.

Answer 1

2) no they cannot have because HCF should be a factor of LCM
1) let's assume it is rational
√13+√17=p/q
squaring on both sides
13+17+2√221=p^2/q^2
√221=p^2+30q^2/2q^2
LHS is irrational
RHS is rational
but rational is not irrational
so this contradicts our assumption that it is rational
so it's irrational
hope this helps you