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Honors Math 2 Definition and Properties of Square Roots (Sections 1.02-1.04) Definition: If r ≥ 0 , the square root 1. s ≥ 0 2. s2 = r Name: Date: r is a real number s such that: € (NOTE:€Your textbook sometimes calls this the “Duck Principle”) € € nonnegative real number has exactly one square root. Postulate: Every Examples: Use the definition of a square root to prove 49 = 7 . € Use the definition of a square root to prove 5= 10 . 2 € Is the conjecture x 2 = x true for all real numbers x? € Theorem: If x and y are nonnegative numbers, then Proof: € x⋅ y = xy . Theorem: If a and b are nonnegative numbers with b ≠ 0 , then a a = . b b Proof: € Is the conjecture € a + b = a + b true for all nonnegative numbers a and b? € Conventions for Square Roots • Simplify all square roots – replace perfect squares inside the square root sign with their square roots outside the square root sign. • Do not leave a square root sign in the denominator. Examples: 50 € 1 3 € 48 − 3 € For You to Do 1. Simplify the expression by combining like terms. 3 2 − 6 5 − 1.25 2 − 2 17 + 8 5 + 1.25 2 + 2 6 + 6 2. Write each square root in simplified form by finding perfect squares in the number under the symbol. 32 92 20 1800 3. Write each fraction in simplified form by eliminating the square root in the denominator. ! ! !! ! ! !! ! Homework: page 10 #2, 8 page 14 #1, 2, 5, 6 page 18 #2, 5, 6 (Reminder: When textbook says “Duck Principle,” it means the definition of square root)