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#### bergausstein

##### Active member
can you tell the difference

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

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

#### MarkFL

Staff member
Use the definition:

$$\displaystyle |x|\equiv\sqrt{x^2}$$

Hence:

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

#### HallsofIvy

##### Well-known member
MHB Math Helper
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 $$(1)^2$$ and $$(-1)^2$$ are equal to 1 so both of those is $$\sqrt{1}$$. And $$\sqrt{a}$$ is defined as the positive number, x, such that $$x^2= 1$$.