Radical Expressions definitions Flashcards
Radical Expressions definitions
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Square Root A value that, when multiplied by itself, yields the original positive number; always two for positive numbers: one positive, one negative. Radical Symbol A notation used to indicate the root of a number, with the default meaning being the positive root unless a negative sign is present. Principal Root The positive value obtained from a radical expression, indicated by the radical symbol without a negative sign. Negative Root The negative value associated with a radical, shown by placing a minus sign in front of the radical symbol. Radicand The number or expression located inside the radical symbol, whose root is being determined. Index A small number written at the upper left of the radical symbol, indicating which root is being taken. Nth Root A value that, when raised to the nth power, equals the original number; generalizes square and cube roots. Even Index A root with an index that is an even number, resulting in two real roots for positive radicands and imaginary results for negative radicands. Odd Index A root with an index that is an odd number, allowing both positive and negative radicands to yield real roots matching the sign of the radicand. Imaginary Number A result that occurs when taking an even root of a negative radicand, indicating no real solution exists. Cube Root A value that, when used three times in multiplication, produces the original number; always one real root matching the radicand's sign. Perfect Power A number that can be expressed as an integer raised to an integer exponent, such as perfect squares or cubes. Exponent A number indicating how many times a base is multiplied by itself; used in relation to roots as the inverse operation. Shortcut Rule A method where, if the exponent inside a radical matches the index, the radical and exponent cancel, leaving the base.
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