Which of these four points lies closest to the origin?

Compare the squared distances $x^2+y^2$; no square roots are needed, because a larger square always belongs to a larger distance. (3, 5) gives 9 + 25 = 34, (-4, 4) gives 16 + 16 = 32, (5, 2) gives 25 + 4 = 29 and (1, -6) gives 1 + 36 = 37. The smallest is 29, so (5, 2) is closest, at $\sqrt{29}\approx 5.39$ units. The minus sign in (-4, 4) does not shorten anything, since it is squared away.