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SQUARE ROOTS Principle square roots – Imperfect square roots A square root is the product of 2 identical numbers Example: the square of 7 is (72) which is equal to 7 x 7 = 49 Activity: a) 92 e) 122 b) 112 f) 62 c) 42 g) the square of 30 = d) 172 h) 72 - 62 = i) 2(4)2 + 3(22) = m) 50 – 32 x 5 = j) 6(32) - 2(52) = n) 6 x 52 -- 5 x 42 k) 12 + 22 = 32 = o) 16 + 3 x 72 l) 8 x 32 12 = Finding the Square Root is the opposite of finding the square. 52 = 5 x 5 = 25 25 = 5 100 means _____ x _____ = 100 these two numbers must be the same ACTIVITY: Do together orally) a) 144 12 122 = 144 b) 36 6 62 = 36 c) 400 d) 16 e) 64 20 4 8 202 = 400 42 = 16 82 = 64 Have the students write the squares from 1 – 25 Square Roots Perfect square – imperfect square roots Principle square root One of two equal factors of a number. Example: The 16 = 4 x 4 Any positive real number has two square roots. Example: The 16 = 4 and – 4 Because 4 x 4 = 16 and - 4 x - 4 = 16 The positive square root is called the Principle Square Root. Example: The square root of 25 is real +25 and -25 The principle square root of 25 is +25 There are 4 ways to calculate square root ( Calculator Mental computations ). Estimating Factoring (prime factorization) ACTIVITY: 1. 100 - 49 = _________________________ 2. 64 + 36 = _________________________ 3. 49 - 81 = _________________________ 4. 5. 1 - 25 + 64 36 - 144 = = __________________ _________________________ ESTIMATING SQUARE ROOTS. Most numbers like 85, do not have a perfect square root. Example: The square root of 81 = 9 The square root of 100 = 10 The square root can be approximated using a divide-and- average method. To find the square root of a number accurate to a specific number of decimal places, follow these steps: 1. Estimate the integer whose square is closest to the number. 2. Divide the number by your estimate and calculate a quotient with two more decimal places than the divisor (the estimate). 3. Find the average of the divisor (estimate) and the quotient. Ex: Find the positive square root of 85 to the nearest hundredth. 1. Estimate 9, because 9 x 9 = 81 2. 85 = 9.44 9 3. 9 + 9.44 = 9.22 2 The square root of 85 = 9.22 (to the nearest hundredth) ACTIVITY: Estimate the integer whose square is closest to the number. a) 50 __________________ b) 150 __________________ c) 500 __________________ d) 1500 __________________ Find the positive square root to the nearest hundredth. a) 28 b) 72 ______________________________________________ ______________________________________________ ______________________________________________ ____________________________________________ Find the positive square root to the nearest thousandth. a) 2 b) 5 c) 12 ______________________________________________ ______________________________________________ ______________________________________________ ______________________________________________ ______________________________________________ ______________________________________________ ______________________________________________ ______________________________________________