Question

`2sqrt(3)` is ______.

Options

• an integer

• a rational number

• an irrational number

• a whole number

Answer 1

`2sqrt(3)` is an irrational number.

Explanation:

Let us assume that `2sqrt(3)` is a rational number = r

i.e., `2sqrt(3) = r`

⇒ `sqrt(3) = r/2`

Now, we know that `sqrt(3)` is an irrational number.

So, `r/2` has to be irrational to make the equation true. This is a contradiction to our assumption. Thus, our assumption is wrong and `2sqrt(3)` is an irrational number.