The discussion centers on the mathematical evaluation of square roots, specifically addressing the expressions $\displaystyle \sqrt{(1)^2}$ and $\displaystyle \sqrt{(-1)^2}$. It is established that both expressions equal 1, as both (1)^2 and (-1)^2 yield 1. However, the discussion emphasizes that the square root function, defined as $\sqrt{a}$, returns only the principal (positive) root, which is 1 in this case. The conclusion is that the correct interpretation of $\sqrt{(-1)^2}$ is indeed 1, not -1.
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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.bergausstein said:can you tell the difference
$\displaystyle \sqrt{(1)^2}=1$$\displaystyle \sqrt{(-1)^2}=-1$