1. 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

2. 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)

3. 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)

4. 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

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

6. 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

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

8. 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!

9. 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

10. 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

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

12. Algebra 9.1 Square Roots Lesson Quiz Find the two square roots of each number. 1. 81 2. 2500 9950