1. Find the two square roots of each number. Exploring Square Roots and Irrational Numbers COURSE 3 LESSON 4-8 a. 81 9 9 = 81 –9 (–9) = 81 The two square roots of 81 are 9 and –9. b. 1 36 1616 1616 –– = 1 36 The two square roots of are and –. 1616 1616 1 36 1616 1616 = 1 36 4-8

2. Estimate the value of – 70 to the nearest integer. Exploring Square Roots and Irrational Numbers COURSE 3 LESSON 4-8 Since 70 is closer to 64 than it is to 81, – 70 –8. 4-8

3. The math class drops a small ball from the top of a stairwell. They measure the distance to the basement as 48 feet. Use the formula d = 16t 2 to find how long it takes the ball to fall. Exploring Square Roots and Irrational Numbers COURSE 3 LESSON 4-8 48 = 16t 2 Substitute 48 for d. d = 16t 2 Use the formula. = t 2 Divide each side by 16. 48 16 3 = t 2 Simplify. 4-8

4. (continued) Exploring Square Roots and Irrational Numbers COURSE 3 LESSON 4-8 It takes about 1.7 seconds for the ball to fall 48 ft. 3 = tFind the positive square root. Use a calculator.31.7320508 Round to the nearest tenth.1.7 t 4-8

5. Identify each number as rational or irrational. Explain. Exploring Square Roots and Irrational Numbers COURSE 3 LESSON 4-8 d. 6.36366366636666... Irrational; the decimal does not terminate or repeat. Rational; the decimal repeats.a. –9.3333 b. 4 7979 Rational; the number can be written as the ratio. 43 9 Irrational; 90 is not a perfect square. c. 90 4-8

6. 1.Find the two square roots of 400. 2.Estimate 34 to the nearest integer. 3.Using d = 16t 2, find how long it takes a skydiver to fall 676 ft from an airplane. 4.Is rational or irrational? Explain. Exploring Square Roots and Irrational Numbers 20 and –20 6 COURSE 3 LESSON 4-8 6.5 s Rational; it can be written as. 8585 64 5 4-8