EVOLUTION; OR EXTRACTION OF ROOTS.The root of any given number, or power, is such a number, as being multiplied by itself a certain number of times, will produce the power; and it is denominated the first, second, third, fourth, &c. root, respectively, as the number of multiplications made of it to produce the given power is 0, 1, 2, 3, &c. that is, the name of the root is taken from the number which exceeds the multiplications by 1, like the name of the power in involution.The index of the root, like that of the power in involution, is 1 more than the number of the multi∣plications necessary to produce the power or given number. So 2 is the index of the second or square root; and 3 the index of the 3d or cubic root; and 4 the index of the 4th root; and so on.Roots are sometimes denoted by writing √ before the power, with the index of the root against it: so the third root of 50 is 3√50, and the second root of it is √50, the index 2 being omitted, which index is always understood when a root is named or written without one, but if the power be expressed by several numbers with the sign + or −, &c. between them, then a line is drawn from the top of the sign of the root or radical sign, over all the parts of it; so the third root of 47−15 is . and sometimes roots are designed like powers, with the reciprocal or 0