square root

Any value multiplied by itself is a square. If that value is multiplied by itself and then by itself again, it is termed a cube. Squares and cubes are represented by the exponent powers 2 and 3 respectively. The reverse operations to squaring and cubing would be finding the square root and finding the cube root.

Number that when it is squared (multiplied by itself) equals a given number. For example, the square root of 25 (written as √25) is +5 or −5. This is because +5 × +5 = 25, and −5 × −5 = 25. A square root can be written as 1/2. For example, = +4 or = −4. This is called an exponent.

Negative numbers (less than 0) do not have square roots that are real numbers. Their roots are represented by complex numbers, in which the square root of −1 is given the symbol i (that is, ± i² = −1). All square roots generate two answers and complex square roots occur in conjugate pairs, that is, √(a + ib) = c ± id. Thus the square root of −4 is √[(−1) × 4] = √−1 × √4 = ±2i.