Expressions that have the square root sign are said to be radicals.
The simplified form of [tex]-6i\sqrt{-44}[/tex] is [tex]12\sqrt{11}[/tex]
The expression is given as:
[tex]-6i\sqrt{-44}[/tex]
Start by splitting the expression
[tex]-6i\sqrt{-44} = -6 \times i \times \sqrt{-44}[/tex]
Factorize -44
[tex]-6i\sqrt{-44} = -6 \times i \times \sqrt{-1} \times \sqrt{44}[/tex]
In complex numbers;
[tex]i = \sqrt{-1[/tex]
So, we have:
[tex]-6i\sqrt{-44} = -6 \times \sqrt{-1} \times \sqrt{-1} \times \sqrt{44}[/tex]
Express [tex]\sqrt{-1} \times \sqrt{-1}[/tex] as [tex]-1[/tex]
[tex]-6i\sqrt{-44} = -6 \times -1 \times \sqrt{44}[/tex]
[tex]-6i\sqrt{-44} = 6 \times \sqrt{44}[/tex]
Express 44 as 4 x 11
[tex]-6i\sqrt{-44} = 6 \times \sqrt{4} \times \sqrt{11}[/tex]
Express [tex]\sqrt 4[/tex] as [tex]2[/tex]
[tex]-6i\sqrt{-44} = 6 \times 2 \times \sqrt{11}[/tex]
[tex]-6i\sqrt{-44} = 12 \times \sqrt{11}[/tex]
[tex]-6i\sqrt{-44} = 12\sqrt{11}[/tex]
Hence, the simplified expression is: [tex]12\sqrt{11}[/tex]
Read more about radical expressions at:
https://brainly.com/question/1810591
