(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.
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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
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
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