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, No. 41.

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 4; the cube-root of 8; the biquadrate root of 16, &c.

Roots of an equation, denotes the value of the unknown quantity in an equation, which issue aquanty, 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 $3x^2 + 5 = 14$, 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 $\sqrt{-a^2}$, is imaginary or impossible, because there is no quantity, neither $+a$ nor $-a$, which by squaring will make the given negative square $-a^2$.