Simplify radical expressions with variables

Question

√243x^2

I can easily deduce 9x√3

Though the true answer is 9 |x| √3

Reducing these problems for the most part is pretty simple for me. I usually use a factor tree and that seems to work it out. My question is....I am having trouble understanding when to take the absolute value of any term....in the example provided |x|.

I know it has something to do with the index and whether an answer can be positive or negative, but am still struggling.

Can anyone provide a simple way to understand this concept? Please feel free to use the example I provided or another example for ease of explanation.

Thanks,

Brian

Answer 1

For example, √(3²) = 3 and √((-3)²) = 3 = l -3 l

So, if x > 0, then √(x²) = x, On the other hand, if x < 0, then √(x²) = l x l