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Lesson 3-1 Square Roots Find each square root: 1. 81 Perfect squares – Numbers that can be pictured in squares of dots. 2. 144 3. Square Root – the number of dots in each row or column in the square. 49 If x2 = y, then x is a square root of y. 4. 225 5. 0.16 Principal square root – the positive square root of a number. Radical sign – the symbol . 25 = 5 - 25 = -5 Solve: 6. x 2 49 64 To find the square root of large numbers, do upside down division. 225 = 3 3 5 5, so sq. root = 15. 7. 4 y2 25 8. a 2 196 To find the square root of fractions, just find the square root of each part. Your answer will be a fraction. Reduce. 9 = 3 4 16 9. 0.09 m 2 Glencoe Math App & Conn (2006) – Course 3 Lesson 3-2 Estimating Square Roots Estimate to the nearest whole number: 1. 54 2. 35 Estimate square roots – Figure out which two perfect squares the number is between. Name the square root that is closest. 79 is between 64 and 81 . Subtract to find the closest one. 3. 170 4. 14.8 79 – 64 = 15 and 81 – 79 = 2, so 9 is the closest square root. For fractions and decimals, do the same thing. 5. If you were to invest $100 in a bank account for two years, your money would earn interest daily and be worth more when you withdrew it. If you had $120 after two years, the interest rate, written as a decimal, would be found 120 10 using the expression . 10 Estimate this value. Glencoe Math App & Conn (2006) – Course 3 Lesson 3-3 The Real Number System Name all sets of numbers to which each real number belongs: 1. 25 Real Numbers – include rational and irrational numbers. Rational Numbers Irrational Integers 2. 12 Whole 3. 0.090909… 4. Estimate 8 and 2 to the nearest tenth. Then graph on a number line. Irrational Numbers – a number that cannot be expressed as a fraction. 0.6666…. is rational because we can change it into a fraction. -2 -1 0 1 2 3 4 Compare to make a true sentence: 7 29 5. 3 8 3 is whole, integer, rational, real. -4 is integer, rational, real. 3 is rational, real. 2 29 is irrational. 6. 3.2 10.4 7. The time in seconds that it takes an object to fall d feet is 0.25 d . How many seconds would it take for a baseball that is hit 250 feet straight up in the air to fall from its highest point to the ground? Glencoe Math App & Conn (2006) – Course 3 Lesson 3-4 The Pythagorean Theorem Hypotenuse – opposite of the right angle. 1. Find the length of the kite string. c ft. 12 ft. Legs – The sides that form the right angle. hypotenuse leg 5 ft. 2. The hypotenuse of a right triangle is 33 centimeters long and one of its legs is 28 centimeters. Find the length of the other leg. leg Pythagorean Theorem: a2 + b2 = c2 5 ft. 3. A 10-foot ramp is extended from the back of a truck to the ground to help movers load furniture onto the truck. If the ramp touches the ground at a point 9 feet behind the truck, how high off the ground is the top of the ramp? a. about 1 foot c. about 13.5 feet b. about 4.4 feet c. about 19 feet 4. The measures of three sides of a triangle are 24 inches, 7 inches, and 25 inches. Determine whether the triangle is a right triangle. 12 ft. 52 + 122 = c2 25 + 144 = c2 169 = c2 169 = 13 ft. To determine if 3 sides form a right triangle use Pythagorean Theorem: 1) Use the 2 smaller numbers for a and b . 2) Use the largest number for c. 15 in., 8 in., 17 in. 152 + 82 = 172 225 + 64 = 289 289 = 289 Glencoe Math App & Conn (2006) – Course 3 Lesson 3-5 Using the Pythagorean Theorem Same as yesterday: 1. A ramp to the entrance of a newly constructed building must be built according to accessibility guidelines stated in the Americans with Disabilities Act. If the ramp is 24.1 feet long and the top of the ramp is 2 feet off the ground, how far is the end of the ramp from the entrance? Pythagorean Theorem: a2 + b2 = c2 2. Multiply the triple 5-12-13 by the numbers 2, 3, 4 to find more Pythagorean triples. 3. To save energy in a cold climate, a house has a roof that slants from the middle of the house to the ground on the north side. The house is 48 feet wide and 18 feet tall. How long is the roof? r ft 18 ft. 48 ft. Glencoe Math App & Conn (2006) – Course 3 Lesson 3-6 Geometry: Distance on the Coordinate Plane 1. Graph the ordered pairs (0, -6) and (5, -1). Then find the distance between the two points. 2. Graph the ordered pairs (-1, 2) and (7, -4) on a coordinate plane. Then find the distance between the points. Use Pythagorean Theorem to find the distance between two points on the x-y coordinate system. Steps: 1. Graph the two points. 2. Draw a horizontal and vertical line until the two meet. 3. Count the squares to find the length of the two legs. 4. Use Pythagorean Theorem to find the length between the two points. Pythagorean Theorem: a2 + b2 = c2 • 4 • 3 To find the distance between (0, -1) and (3, 3). 1. Graph the two points. 2. Draw a horizontal & vertical line. 3. Count the spaces; 4 and 3. 4. 42 + 32 = c2 25 = c2 16 + 9 = c2 25 = c 5=c Glencoe Math App & Conn (2006) – Course 3