Question

`(1 + sqrt3)^2 -  (1 - sqrt3)^2` is ______.

Options

• a positive rational number

• a negative integer

• a positive irrational number

• a negative irrational number

Answer 1

`(1 + sqrt3)^2 -  (1 - sqrt3)^2` is a positive irrational number.

Explanation:

`(1 + sqrt3)^2 -  (1 - sqrt3)^2`

= `(1 + 3 + 2 sqrt3) - (1 + 3 - 2 sqrt3)`

= `4 + 2 sqrt3 - 4 + 2 sqrt3`

= `4sqrt3`

A positive irrational number.