Question

give that root 2 is irrational prove that (5+3root2 is an rational number

Answer 1

given
$\sqrt{2}$
is irrational
then
if possible
$5 \times 3 \sqrt{2}$
be a rational no.

$5 \times 3 \sqrt{2} = \frac{p}{q}$
we get
$\sqrt{2 } = \frac{p}{q} \times \frac{1}{15}$
given that root 2 is irrational and here it is rational
hence it is not possible, so 5 x 3root2 is irrational
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