State the following statement is true or false
True
False
$3\sqrt{18}=9\sqrt{2},$ which is the product of a rational and an irrational number and so an irrational number.
$6+\sqrt{2}$ is a rational number.
Let's assume that $6+\sqrt2$ is rational..... then $6+\sqrt2 = p/q $$\sqrt2 =( p-6q)/(q) $ now take $p-6q$ to be P and $q$ to be Q........where P and Q are integers which means, $\sqrt2= P/Q$...... But this contradicts the fact that $\sqrt2$ is rational So our assumption is wrong and $6+\sqrt2$ is irrational.