ROOT

ROOT, among botanists, denotes that part of a plant.

plant which imbibes the nutritious juices of the earth, and transmits them to the other parts. See PLANT and RADIX.

Colour extracted from Roots. See COLOUR Making, N^o 41.

Root, in Algebra and Arithmetic, denotes any number which, multiplied by itself once or oftener, produces any other number; and is called the square, cube, biquadrate, &c. root, according to the number of multiplications. Thus, 2 is the square of $\backslash frac\{1\}\{2\}$; the cube-root of 8; the biquadrate root of 16, &c.

Root of an equation, denotes the value of the unknown quantity in an equation, which is such a quantity, as being substituted instead of that unknown letter, into the equation, shall make all the terms to vanish, or both sides equal to each other. Thus, of the equation $3x\; +\; 5\; =\; 14$, the root or value of $x$ is 3, because substituting 3 for $x$ makes it become $9\; +\; 5\; =\; 14$.

Roots, real and imaginary. The odd roots, as the 3d, 5th, 7th, &c. of all real quantities, whether positive or negative, are real and are respectively positive or negative. So the cube root of $a^3$ is $a$, and of $-a^3$ is $-a$. But the even roots, as the 2d, 4th, 6th, &c. are only real when the quantity is positive, being imaginary or impossible when the quantity is negative. So the square root of $a^2$ is $a$, which is real; but the square root of $-a^2$, that is $\backslash sqrt\{-a^2\}$, is imaginary or impossible, because there is no quantity, neither $+a$ nor $-a$, which by squaring will make the given negative square $-a^2$.