Tag: irrational numbers

Questions Related to irrational numbers

State the following statement is true or false

$3\sqrt{18}$ is an irrational number.

  1. True

  2. False


Correct Option: A
Explanation:

$3\sqrt{18}=9\sqrt{2},$ which is the product of a rational and an irrational number and so an irrational number.

$6+\sqrt{2}$ is a rational number.

  1. True

  2. False


Correct Option: B
Explanation:

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.