Roots: square and cube roots and their signs
Count the numbers that square to a positive number, see why a negative has no real square root but does have a cube root, and why the root of a square is the absolute value.
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الدليل
3^2 and (-3)^2 are both 9, so 9 has two square roots, 3 and -3. The symbol √9 gives only the positive one (√9 = 3); the negative one is written -√9.
The square root of zero is zero. A negative number has no square root in the real numbers, since no number squares to a negative.
Every number, positive or negative, has exactly one cube root: ∛8 = 2 and ∛(-8) = -2, since (-2)^3 = -8.
The root of a square is the absolute value: √(a^2) = |a|. So √((-5)^2) = 5, not -5.