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Square Roots Chapter 9.1 page 453 What does it mean? Before--you found squares of numbers. Now--you’ll find and approximate square roots of numbers. Why!!!!!! So you can solve equations. Square Root Websites • http://www.purplemath.com/modules/radicals.htm • http://www.aplusmath.com/games/matho/MultMatho.html • http://www.aplusmath.com/Games/index.html • http://www.aplusmath.com/Flashcards/sqrt.html • http://www.aplusmath.com/Flashcards/index.html • http://www.factmonster.com/ipka/A0875926.html • Divisibility rules websites • http://argyll.epsb.ca/jreed/math7/strand1/1104.htm • http://jc-schools.net/PPT/pfdivisibility.ppt#2 • http://www.nebo.edu/misc/learning_resources/ppt/k- 5/div_rules.ppt#1 • http://www.lessontutor.com/lw6.html Inverse Operations • Every operation has an inverse (opposite). • Subtraction is the inverse of addition. • Division is the inverse of multiplication. • Square roots are the inverse of squaring. • 32 • Describe and give an example of a perfect square. Below is a list of the most common roots. SQUARE CUBE FOURTH • √0 = 0 √49 = 7 ∛0 = 0 4√0 =0 • √1 = 1 √64 = 8 ∛1 = 1 4√1 = 1 • √4 = 2 √81 = 9 ∛8 = 2 4√16 = 2 • √9 = 3 √100 = 10 ∛27 = 3 4√81 = 3 • √16 = 4 √121 = 11 ∛64 = 4 • √25 = 5 √144 = 12 ∛125 = 5 • √36 = 6 √169 = 13 Every positive number has 2 square roots. One is positive and one is negative. • 4 = 2, because 22 = 4 • However, 4 = -2, because (-2)2 = 4 • The radical sign , represents a nonnegative square root. The symbol , read “plus or minus,” refers to both square roots of a positive number. • Because zero is neither positive or negative, it has only one square root, 0. Find the square roots of the number. 1. 4 2. 16 3. 36 4. 64 5. 121 6. 144 7. 225 8. 256 You can use perfect squares to approximate a square root of a number that is not a perfect square. Approximate 51 to the nearest integer • Looking at part of our list of square roots: • 1 = 1 • 4 = 2 • 9 = 3 • =4 • =5 • =6 • =7 • =8 51 is between 49 and 64, and closer to 49 than 64. • Since 49 is 7 and 64 is 8, the 51 is between 7 and 8. • 7 51 8 • So approximating 51 to the nearest integer would be • 7. • Approximate 125 to the nearest whole number. • 92 = • 102 = • 112 = • 122 = Approximate to the nearest integer. 1. 10 2. -84 3. 151 4. -200 Solve the equation. • In September of every even-numbered year, people in Marostica, Italy, play an unusual chess game. Each chess piece is portrayed by a person. The people portraying the knights are even on horseback! • The chessboard is a square with an area of 324 square meters. What is the length of each side of the board? To answer the question, we need to know how to find the area of a square. A = s2 • Since we know the area of the chessboard is 324 m, we substitute that amount into our equation. • A = s2 • 324 = s2 • To solve it, take the square root of both sides. • 324 = s2 • 18 = s Solve the equations. 1. a2 = 9 2. n2 = 25 3. 361 = x2 4. 400 = y2 Radical Expressions • A radical expression is an expression that involves a radical sign. 11 + 52 • 11 + 25 = 36, and 36 = 6 • Always evaluate the expression under the radical sign before finding the square root. • Evaluate 2a + b2, when a = 11 and b = 5. • Substitute 11 in for a and 5 in for b and solve. Evaluate when a = 12 and b = 4. 1. a + b 2. b2 – a 3. 3ab + 1 4. Evaluate when a = 48 and b = 12 a - b An amusement park ride includes a free fall drop of 272 feet. You can use the equation d = 16t2 to determine the time t in seconds that it takes a dropped object to fall a distance of d feet. How long does the free fall part of the ride take? d = 16t2 original equation 272 = 16t2 substituting 272 for d 17 = t2 dividing by 16 17 = t taking the square root 4.1 = t Approximating the sq. rt You can use the following rule of thumb when photographing fireworks. The f-stop, a number that describes the size of the opening of the camera lens, should be the number closest to the square root of the film speed. You have a camera with f-stop numbers 2.8, 4, 5.6, 11, 16, and 22. Which f-stop should you use to photograph fireworks if you are using a film speed of 64? Simplifying Square Roots. Chapter 9.2 page 458 Simplifying a Radical Expression • A radical expression is in simplest form when: a. No factor of the expression under the radical sign () has any perfect square factor. b. There are no fractions under the radical sign, and no radical sign in the denominator of any fraction. • Tell whether the expression 3√5 is in simplest form based on the above criteria. • Yes, because you can’t take the square root of 5. Simplify: • 180 = • 63 = • 98 = • 250 = • 24s2 = • 54t2 = • 300x = • 63b2 = • 75x2y = • 7200m2n2 = Simplify: • 15/16 = • 32/n2 = Simplify: • √11/36 = • √35/144 = Accident Investigation • After a car accident, a police officer measures the length l (in feet) of a car’s skid marks. The expression 27l gives the car’s speed in miles per hour at the time the brakes were applied. • Write the expression 27l in simplest form. • 3•3•3•l Broken down into primes • 33l Pulling out pairs • The length of the skid marks are 125 feet long, so we can substitute that in for l and solve. • 33l = 33(125) • 33•5•5•5 = 3•515 ≈ 15•4 ≈ 60 miles

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