Definition
Square root
A square root of a number is a value that squares to make that number.
What it means
Ask, “What number times itself makes this?” A positive number has two square roots, one positive and one negative, but the √ symbol by itself names only the nonnegative one.
Remember it
Square root asks for one side-factor copied twice.
Example
√81 = 9 because 9 × 9 = 81. The equation y² = 81 has two solutions, y = 9 and y = −9, because both numbers square to 81.
Watch for
Within the real numbers, a negative number has no square root. Later mathematics extends the number system to handle this.
Common mix-up
Do not write √81 = ±9. The ± belongs when solving y² = 81, not in the value of the principal-root symbol.
Exact meaning
A square root of x is a number y such that y² = x. For x ≥ 0, the symbol √x denotes the principal, nonnegative square root.