Question

Simplify ( 2 + sqrt-3 / 2) (2 - sqrt-3 / 2)

Answer 1

`2.5`

Explanation:

The given radical expression is

`(2+\sqrt{-(3)/(2) }) (2-\sqrt{-(3)/(2) })`

Observe that, the given expression can be written as difference of two squares.

That is;
`(x+y)(x-y)=x^2-y^2`

We apply this property to obtain:

`(2+\sqrt{-(3)/(2) }) (2-\sqrt{-(3)/(2) })=2^2-(\sqrt{-(3)/(2) })^2`

We now simplify to get:

`(2+\sqrt{-(3)/(2) }) (2-\sqrt{-(3)/(2) })=4-(3)/(2)`

This simplifies to:

`(2+\sqrt{-(3)/(2) }) (2-\sqrt{-(3)/(2) })=(5)/(2)=2.5`