Radicals and connections to geometry

Transcription

1 Algebra Assignment Sheet Name: Date: Period: # Radicals and connections to geometry (1) Worksheet (need) (2) Page 514 #10 46 Left () Page 514 #1 49 right (4) Page 719 #18 0 Even (5) Page 719 #1 9 all (6) Worksheet 12.2 A (7) Page 766 #4 9, Page 769 #5 8 ***Quiz tomorrow*** (8) Page 725 #15-2 (9) Page 725 #25-28, 6 41 (10) Page #1 odd (11) Page 748 #14 2 even (12) Worksheet *******Quiz tomorrow******* (1) Chapter Practice test *******test tomorrow******* 1

2 Supplement: Perfect Squares and Cubes, Evaluate Sq. Roots and Cube Roots (from 1 to 5 ) (I/1) Perfect Squares: A number whose square roots are integers or quotients of integers 1, 4, 9, 16, 25, 6, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 24, 61, (Integers) x 2, x 4, x 6, x 8, x 10 (Variables) 1/4, 9/25, 4/49, 81/100 (Quotients of Integers) Perfect Cubes: A number whose cube roots are integers or quotients of integers 1, 8, 27, 64, 125, 216, 4, 512, 729, 1000 (Integers) x, x 6, x 9, x 12, x 15 (Variables) 1/8, 64/125, 8/27 (Quotients of Integers) Evaluate: E1) 121 E2) 4 E) 64 E4) 64x 2 E5) 400y 2 z 8 E6) 121x 6 z 12 E7) 9 25 E8) 1 49 E9) 9 49 E10) 9x2 25 E11) y8 49 E12) 4z20 81 E1) 27 E14) 8 E15) 125 E16) 8x 6 E17) 4w z 9 E18) 1000x 21 E19) w9 64 E20) 27x E21) w24 z 12 2

3 9.2 Simplifying Radicals (I,E/2) An expression with radicals is in if the following are true: 1) All radicals are broken down 2) All coefficients are reduced ) No radicals are in the denominator Helpful Hint: It is often easier to break down radicals first in an attempt to make the numbers more manageable. E1) Simplify the expression 50 P1) Simplify the expression 48 E2) Simplify the expression a. 4 b c P2) Simplify the expression a b. 18 c E) Simplify the expression 8wx 5 y z 10 P) Simplify the expression 150x 8 y 5 z 1

4 12.2 Operations with Radical Expressions (Add/Sub/Mult/Rationalize) (I,E/4) E1) Simplify a b P1) Simplify a b E2) Simplify a. 2 8 b. 2(5 ) c. (1 + 5) 2 d. (a b)(a + b) P2) Simplify a. 12 b. (7 + 5) c. (1 ) 2 d. (6 2)(6 + 2) E) Simplify (conjugates are optional) a. 5 b. 1 c d P) Simplify (conjugates are optional) a. 1 b

5 12. Solving Radical Equations (I,E/2) Steps to Solving Radical Equations: 1. Isolate the radical 2. Use inverse operations to eliminate the radical. Solve the equation 4. Check the solution(s) for any extraneous solutions E1) Solve x 7 = 0 P1) Solve x 10 = 0 E2) Solve 2x + = 4 P2) Solve x = 6 E) Solve a. x + 2 = x b. x + 1 = 0 P) Solve a. 4x = x b. x + 9 = 0 5

6 12.5 and 12.6 Pythagorean Theorem with Apps and Distance Formula (R,E/) A is a statement that can be proven to be true. In mathematics an if-then statement is a statement of the form if p, then q, where p is the and q is the. The of the statement if p, then q is the related statement if q, then p, in which the hypothesis and conclusion are interchanged. The converse of the Pythagorean Theorem is also true. E1) Using the Pythagorean Theorem (use the right triangle above) a. Given a=6 and b=8, find c. b. Given a = 5 and c = 6, find b. P1) Using the Pythagorean Theorem (use the right triangle above) a. Given a=8 and b=15, find c. b. Given a = 2 and c = 7, find b. E2) A right triangle has one leg that is inches longer than the other leg. The hypotenuse is 15 inches. Find the missing lengths. 6

7 P2) A right triangle has a hypotenuse that is 1 foot longer than the longer leg. The shorter leg is 9 feet. Find the missing lengths. E) Determine whether the given lengths are sides of a right triangle. a. 11.9, 12.0, 16.9 b. 5, 11, 12 P) Determine whether the given lengths are sides of a right triangle. a. 0.5, 0.8, 1.0 b. 20, 21, 29 E4) The length of each side of a baseball diamond is 90 feet. What is the distance from home plate to second base? P4) A ladder 8 m long is resting against a building. The bottom of the ladder is m from the wall. To the nearest tenth, how far up the wall does the ladder reach? The Distance Formula: The distance formula can be derived by applying the Pythagorean theorem to a right triangle in a coordinate plane. The distance d between two points (x 1, y 1) and (x 2, y 2) is: d = (x 2 x 1 ) 2 + (y 2 y 1 ) 2 7

8 Side Line E6) Find the distance between (1, 4) and (-2, ). P6) Find the distance between (,-1) and (4, 0). E7) Decide whether the points (, 2), (2, 0) and (-1, 4) are vertices of a right triangle. P7) Decide whether the points (-2, ), (-1, 1) and (2, ) are vertices of a right triangle. E8) A player kicks a soccer ball from a position that is 10 yards from a sideline and 5 yards from a goal line. The ball lands at a position that is 45 yards from the same goal line and 40 yards from the same sideline. How far was the ball kicked? Soccer Goal Line P8) A player kicks a soccer ball from a position that is 8 yards from a sideline and 15 yards from a goal line. The ball lands at a position that is 0 yards from the same goal line and 55 yards from the same sideline. How far was the ball kicked? 8