Radical

[bergausstein]

can you tell the difference

$\displaystyle \sqrt{(1)^2}=1$


$\displaystyle \sqrt{(-1)^2}=-1$

 

[MarkFL]

Use the definition:

\(\displaystyle |x|\equiv\sqrt{x^2}\)

Hence:

\(\displaystyle \sqrt{(-1)^2}=|-1|=1\)

 

[HallsofIvy]

can you tell the difference

$\displaystyle \sqrt{(1)^2}=1$


$\displaystyle \sqrt{(-1)^2}=-1$

The major difference is that the first one is right and the second one is wrong! Both [tex](1)^2[/tex] and [tex](-1)^2[/tex] are equal to 1 so both of those is [tex]\sqrt{1}[/tex]. And [tex]\sqrt{a}[/tex] is defined as the positive number, x, such that [tex]x^2= 1[/tex].