Answer:
3i[tex]\sqrt{5}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
and [tex]\sqrt{-1}[/tex] = i
Given
[tex]\sqrt{-45}[/tex]
= [tex]\sqrt{9(5)(-1)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex] × [tex]\sqrt{-1}[/tex]
= 3 × [tex]\sqrt{5}[/tex] × i
= 3i[tex]\sqrt{5}[/tex]
