Question

(i) `(sqrt(3) + 1)/(sqrt(3) - 1) = 2 + sqrt(3)`.

(ii) `22/7` is an irrational number.

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Only (i)

Explanation:

(i) `(sqrt(3) + 1)/(sqrt(3) - 1) = 2 + sqrt(3)`

Let’s verify this:

`(sqrt(3) + 1)/(sqrt(3) - 1) xx (sqrt(3) + 1)/(sqrt(3) + 1)`

= `(sqrt(3) + 1)^2/((sqrt(3))^2 - 1^2)`

= `(3 + 1 + 2sqrt(3))/(3 - 1)`

= `(4 + 2sqrt(3))/2`

= `2 + sqrt(3)`

So statement (i) is true.

(ii) `22/7` is an irrational number.

This is false because `22/7` is a rational number it’s a fraction of two integers.

Hence, only statement (i) is valid.