Answer:
[tex]2.5[/tex]
Step-by-step explanation:
The given radical expression is
[tex](2+\sqrt{-\frac{3}{2} }) (2-\sqrt{-\frac{3}{2} })[/tex]
Observe that, the given expression can be written as difference of two squares.
That is; [tex](x+y)(x-y)=x^2-y^2[/tex]
We apply this property to obtain:
[tex](2+\sqrt{-\frac{3}{2} }) (2-\sqrt{-\frac{3}{2} })=2^2-(\sqrt{-\frac{3}{2} })^2[/tex]
We now simplify to get:
[tex](2+\sqrt{-\frac{3}{2} }) (2-\sqrt{-\frac{3}{2} })=4-\frac{3}{2}[/tex]
This simplifies to:
[tex](2+\sqrt{-\frac{3}{2} }) (2-\sqrt{-\frac{3}{2} })=\frac{5}{2}=2.5[/tex]
