Answer: [tex]6y^2i\sqrt{6}[/tex]
Step-by-step explanation:
For this exercise it is important to remember the following property:
[tex]\sqrt[n]{a^n}=a^{({\frac{n}{n})}}=a[/tex]
Then, given the expression:
[tex]\sqrt{-216y^4}[/tex]
You can follow these steps in order to simplify it:
1. Descompose 216 into its prime factors:
[tex]216=2*2*2*3*3*3[/tex]
2. The Product of powers property states that:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
Then:
[tex]216=2^2*2*3^2*3[/tex]
3. Now you can substitute:
[tex]=\sqrt{-2^2*2*3^2*3*y^4}[/tex]
4. Finally, substituting [tex]\sqrt{-1}=i[/tex] and simplifying, you get:
[tex]=2*3*y^2i\sqrt{2*3}=6y^2i\sqrt{6}[/tex]
