[tex]$\frac{3}{4} \sqrt{-80}$[/tex]
Step-by-step explanation:
Given data: [tex]$\frac{3}{4} \sqrt{-80}$[/tex]
We find the equivalent value the expression [tex]$\frac{3}{4} \sqrt{-80}$[/tex].
The value –80 can be written as –1 × 16 × 5.
Now, substitute the value of –80 in the given expression.
[tex]$\frac{3}{4} \sqrt{-80}=\frac{3}{4} \sqrt{-1 \times 16 \times 5}$[/tex]
[tex]=\frac{3}{4} \sqrt{-1 \times 4^{2} \times 5}[/tex] (16 is the square number of 4)
[tex]=\frac{3}{4} \times 4 \sqrt{-1 \times 5}[/tex] (Square number can be taken out)
[tex]=3 \sqrt{-1 \times 5}[/tex] (4 in the numerator and denominator are cancel)
Since[tex]\sqrt{-1}=i[/tex],
[tex]=3i\sqrt{5}[/tex]
So, the expression [tex]$\frac{3}{4} \sqrt{-80}$[/tex] is equivalent to [tex]3i\sqrt{5}[/tex].
