Answer:
6i[tex]\sqrt{21}[/tex]
Step-by-step explanation:
Note that [tex]\sqrt{-1}[/tex] = i
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Simplifying the radical, that is
[tex]\sqrt{-84}[/tex]
= [tex]\sqrt{4(21)(-1)}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{21}[/tex] × [tex]\sqrt{-1}[/tex]
= 2 × [tex]\sqrt{21}[/tex] × i
= 2i[tex]\sqrt{21}[/tex]
Hence
3[tex]\sqrt{-84}[/tex]
= 3 × 2i[tex]\sqrt{21}[/tex]
= 6i[tex]\sqrt{21}[/tex]
