Answer:
[tex]-4|x|[/tex]
Step-by-step explanation:
To simplify :
[tex]-\sqrt{16x^2}[/tex] , when [tex]x<0[/tex]
In order to simplify the given expression we will take the square root of the term inside the root.
The term in the square root are perfect squares (square of an integer), so, we can write them in square of the numbers.
⇒ [tex]-\sqrt{(\pm4x)^2}[/tex] [As [tex](\pm4x)^2=16x^2[/tex]]
On taking square root the square gets removed. So, we have,
⇒ [tex]-(\pm4x)[/tex]
⇒ [tex]-4|x|[/tex]
Since [tex]x<0[/tex], so the value would be negative.
So, simplified answer is
[tex]-4|x|[/tex] (Answer)
