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9.2 – Simplifying Radicals Today we will be learning how to: Use properties of radicals to simplify radicals Use quadratic equations to model real-life problems Evaluate the radical expressions √ab and √a √b for the given values of a and b. a = 4, b = 9 a = 25, b = 4 a = 36, b = 16 Evaluate the radical expressions given values of a and b. a = 4, b = 49 a = 16, b = 64 a = 144, b = 100 a and b a b for the Product Property The square root of a product equals the product of the square roots of the factors. √ab = √a √b where a ≥ 0 and b ≥ 0 Ex. √4 100 = √4 √100 Quotient Property The square root of a quotient equals the quotient of the square roots of the numerator and denominator. a a b b Ex. where a ≥ 0 and b > 0 9 9 25 25 An expression is in simplest form if: No perfect square factors other than 1 are in the radicand √8 = √42 = 2√2 No fractions are in the radicand 5 5 5 16 4 16 No radicals appear in the denominator of a fraction 1 1 4 2 Example 1 Simplify the expression √48 Example 2 Simplify the expression 7 16 18 3 80 45 Example 3 The distance d you can see to the horizon depends on your height h. A model is d2 = 1.5h, with d in miles and h in feet. Find the exact distance you can see from the top of a 400 ft building. Example 3 The distance d you can see to the horizon depends on your height h. A model is d2 = 1.5h, with d in miles and h in feet. Find the distance in part 1 to the nearest tenth. Example 3 The distance d you can see to the horizon depends on your height h. A model is d2 = 1.5h, with d in miles and h in feet. If you were 3 × 400 = 1200 ft up in a skyscraper, how far could you see to the nearest tenth? HOMEWORK Page 514 #10 – 48 even