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Algebra 9.1 Square Roots I will use the inverse of perfect squares to find approximate values of square roots. I will use square roots to evaluate radical expressions and solve equations. Algebra Objective

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Algebra 9.1 Square Roots Vocabulary Square root - a number n such that if multiplied by itself, it is equal to a perfect square - n 2 = x, where x is a perfect square - the inverse of squaring a number - all positive numbers have two square roots (1 positive, 1 negative)

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Algebra 9.1 Square Roots Vocabulary Perfect square - a number that is a square of an integer - Examples: 1, 4, 9, 16, 25… Radicand - the number or expression inside a radical symbol Irrational Number - a number that cannot be written as the quotient of two integers (example: square roots) Radical Expression - an expression with a square root (or radical)

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Algebra 9.1 Square Roots Think about the relationship between the area of a square and the length of one of its sides. Taking the square root of a number is the inverse of squaring the number. area = 36 square units side length = 36 = 6 units 6 2 = 36 36 = 6

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Algebra 9.1 Square Roots –49 is not the same as – 49. A negative number has no real square root. Caution!

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Algebra 9.1 Square Roots A. 25 5 is a square root, since 5 5 = 25. –5 is also a square root, since –5 –5 = 25. Rewrite as 12 is a square root, since 12 12 = 144. –12 is also a square root, since –12 –12 = 144. Rewrite as Find the two square roots of each number. B. 144

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Algebra 9.1 Square Roots A. 49 Guided Practice Find the two square roots of each number. B. 225

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Algebra 9.1 Square Roots 13 2 = 169 The window is 13 inches wide. Find the square root of 169 to find the width of the window. Use the positive square root; a negative length has no meaning. Example 2: Application A square window has an area of 169 square inches. How wide is the window? So 169 = 13. The area of a square is s 2, where s is the length of a side. Remember!

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Algebra 9.1 Square Roots Approximating a Square Root To approximate a square root - choose one perfect square less than the number and one perfect square greater than the number - take the square root of the perfect square of that is nearest to the original number

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Algebra 9.1 Square Roots Example 3: Approximating a Square Root Find the square root of 78. 64 < 78 < 81Identify the perfect squares closest to 78 78 is closer to 81 than 64. Find the square root of 81

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Algebra 9.1 Square Roots Guided Practice Find the square root of 135.

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Algebra 9.1 Square Roots Lesson Quiz Find the two square roots of each number. 1. 81 2. 2500 9950

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