The correct option is B i.e. [tex]5\frac{1}{2}[/tex].
Step-by-step explanation:
We have the following expression , [tex]\sqrt[3]{343} + \frac{3}{4} \sqrt[3]{-8}[/tex] . As we see the options there aren't in iota or in complex number hence, the correct expression to evaluate must be , [tex]\sqrt[3]{343} + \frac{-3}{4} \sqrt[3]{8}[/tex] . Let's evaluate the expression to simplify:
[tex]\sqrt[3]{343} + \frac{-3}{4} \sqrt[3]{8}[/tex] , its known that [tex]\sqrt[3]{343} = 7[/tex] and [tex]\sqrt[3]{8} = 2[/tex].
⇒ [tex]\sqrt[3]{343} + \frac{-3}{4} \sqrt[3]{8}[/tex]
⇒ [tex]\sqrt[3]{343} - \frac{3}{4} \sqrt[3]{8}[/tex]
⇒ [tex]7 - \frac{3}{4}(2)[/tex]
⇒ [tex]7 - \frac{3}{2}[/tex]
⇒ [tex]\frac{14-3}{2}[/tex]
⇒ [tex]\frac{11}{2} = 5\frac{1}{2}[/tex]
Therefore, the correct option is B i.e. [tex]5\frac{1}{2}[/tex].
