Pre-Calculus 11A 5.1: Radical Operations ________________ value is the ________________ of a point or number from the _________ (zero point) of a number line or coordinate system. The absolute value of c is written as __________ The |c| is defined algebraically as: Examples: Pre-Calculus 11A 5.1: Radical Operations The word "_________" means root. _________ roots, _________ roots, any root expressed with the symbol 3 45 Radical __________ : - an expression involving the __________ __________. The ___________ ____________ of radicals tells us that the ________ ________ of a ________ equals the ________ of the ________ ________ of the ________. Convert each entire radical to a mixed radical in simplest form. a) 300 b) 288 Convert each entire radical as a mixed radical in simplest form a) 40 b) 108 Pre-Calculus 11A 5.1: Radical Operations Principal Square Root For _______ _______ the concept of ___________ _______ must be considered. √(−3)2 = −√(−3)2 = √(3)2 = −√(3)2 = √𝑥 2 = −√𝑥 2 = (- 4)2 or ( 4)2 both equal _____. However √16 = , not ________. By definition, _______defines only the _____________ _______ root ( If we want the negative root, use ( If both roots are required write ( ). ). ). For variable radicands: When the ____________ is a __________, must we consider the concept of a principal root. √(𝑥 − 2)2 = 4 √𝑥 2 + 4𝑥 + 4 = √𝑥 3 = √(2 − 𝑥)4 = For _______ indices: 3 √−8 = 3 √8 =