Estimating Square Roots

Size: px

Start display at page:

Download "Estimating Square Roots"

Bethanie Lindsey
5 years ago
Views:

1 Practice A Estimating Square Roots Each square root is between two consecutive integers. Name the integers. Explain your answer _ _ _ Approximate each square root to the nearest hundredth Use a calculator to find each value. Round to the nearest tenth

2 Practice B Estimating Square Roots Each square root is between two consecutive integers. Name the integers. Explain your answer _ _ The area of a square piece of cardboard is 70 cm². What is the approximate length of each side of the cardboard? Approximate each square root to the nearest hundredth Use a calculator to find each value. Round to the nearest tenth

3 Practice C Estimating Square Roots Each square root is between two consecutive integers. Name the integers. Explain your answer _ _ Use a calculator to find each value. Round to the nearest tenth. Use the indicated letter to graph each point on the number line. 5. A: B: C: D: 0.09 Use guess and check to estimate each square root to the nearest hundredth Find each product to the nearest hundredth ( 16 ) ( 98 ) ( 217 ) 21. If the distance in feet traveled by a falling object is determined by the formula d = 16t 2, in which t is the time in seconds, find the distance a falling object traveled in 22 sec. 22. If the distance traveled by the falling object was 3600 ft, how many seconds did it take to fall?

4 Review for Mastery Estimating Square Roots To locate a square root between two consecutive integers, refer to the table. Number Square Number Square Locate 260 between two integers. 260 is between the perfect squares 256 and 289: 256 < 260 < 289 So: 256 < 260 < 289 And: 16 < 260 < 17 Use the table to complete the statements. 1. < 39 < 2. < 130 < < 39 < < 130 < < 39 < < 130 < After locating a square root between two consecutive integers, you can determine which of the two integers the square root is closer to. 27 is between the perfect squares 25 and 36: 25 < 27 < 36 So: 25 < 27 < 36 And: 5 < 27 < 6 The difference between 27 and 25 is 2; the difference between 36 and 27 is < 27 < 36 So, 27, is closer to Complete the statements < 106 < < 250 < < 106 < < 250 < < 106 < < 250 < = 250 = = 250 = 106 is closer to than 250 is closer to than

5 Challenge Dig Deeper! The digital root of a number is found by adding its digits, adding the digits of the result, and so on, until the result is a single digit = = 9 The digital root of 918 is Complete the table to display numbers and their digital roots and to determine if they are divisible by 3 (remainder = 0). Make an observation about the results. Divisible Digital Root Divisible Number by 3? Calculation by 3? 81 = 92 = 226 = 315 = 659 no = = 2 no 704 = 1064 = 2. Complete the table to display the products of numbers and the products of their digital roots. Make an observation about the results. Product Digital Root of Factor Digital Root of Factor Product of Digital Roots of Factors Digital Root of Product = = = = = = = = = = = =

6 Problem Solving Estimating Square Roots The distance to the horizon can be found using the formula d = h where d is the distance in kilometers and h is the number of kilometers from the ground. Round your answer to the nearest kilometer. 1. How far is it to the horizon when you are standing on the top of Mt. Everest, a height of 8.85 km? 2. Find the distance to the horizon from the top of Mt. McKinley, Alaska, a height of km. 3. How far is it to the horizon if you are standing on the ground and your eyes are 2 m above the ground? _ 4. Mauna Kea is an extinct volcano on Hawaii that is about 4 km tall. You should be able to see the top of Mauna Kea when you are how far away? _ You can find the approximate speed of a vehicle that leaves skid marks before it stops. The formulas S = L and S = L, where S is the speed in miles per hour and L is the length of the skid marks in feet, will give the minimum and maximum speeds that the vehicle was traveling before the brakes were applied. Round to the nearest mile per hour. 5. A vehicle leaves a skid mark of 40 feet before stopping. What was the approximate speed of the vehicle before it stopped? A mi/h C mi/h B mi/h D mi/h 7. A vehicle leaves a skid mark of 150 feet before stopping. What was the approximate speed of the vehicle before it stopped? A mi/h C mi/h B mi/h D mi/h 6. A vehicle leaves a skid mark of 100 feet before stopping. What was the approximate speed of the vehicle before it stopped? F mi/h H mi/h G mi/h J mi/h 8. A vehicle leaves a skid mark of 200 feet before stopping. What was the approximate speed of the vehicle before it stopped? F mi/h H mi/h G mi/h J mi/h

7 Reading Strategies Follow a Procedure The numbers 16 and 25 are called perfect squares. Each has an integer as its square root. To find the square root of a perfect square, ask yourself what number multiplied by itself equals the perfect square. Some Perfect Squares What number times itself equals 16? 2. What is the square root of 16? 3. What number times itself equals 25? 4. What is the square root of 25? Use these steps to estimate the square root of a number that is not a perfect square. What is 45? Step 1 Identify a perfect square that is a little more than The square root of 49 = 7. Step 2 Identify a perfect square that is a little less than The square root of 36 = 6. Step 3 The estimate of 45 is between 6 and 7. Use the steps above to help you estimate the square root of Which perfect square is a little more than 90? 6. What is the square root of 100? 7. Which perfect square is a little less than 90? 8. What is the square root of 81? 9. What is your estimate of the square root of 90?

8 Puzzles, Twisters & Teasers The Root of the Problem! Find the square roots. Use the answers to solve the riddle. S 36 = R 144 = P 100 = T 64 = G 25 = I 9 = W 4 = H 169 = E 81 = U 49 = L 121 = Why can t you play jokes on snakes? Because you can t

9 Answers LESSON 4-6 Practice A 1. 3 and 4; 10 is between 9 and and 3; 8 is between 4 and and 5; 19 is between 16 and and 6; 33 is between 25 and and 4; 15 is between 9 and and 7; 39 is between 36 and Practice B 1. 2 and 3; 6 is between 4 and and 5; 20 is between 16 and and 6; 28 is between 25 and and 7; 44 is between 36 and and 6; 31 is between 25 and and 8; 52 is between 49 and CODE Practice C 1. 8 and 9; 75 is between 64 and and 11; 104 is between 100 and and 14; 180 is between 169 and and 16; 230 is between 225 and ft sec Review for Mastery 1. 36; ; ; ; 144 6; 7 11; ; ; ; ; ; ; 25 10; ; 6 16; 15 Challenge

10 1. A number is divisible by 3 if its digital root is divisible by 3. Div. by 3 Calculation Root Div. by 3 yes yes no = 11 2 no no = no yes yes no = no 1 no = no 2. The digital root of a product of whole numbers equals the product of the digital roots of the factors. Product Digital Root of Factor Digital Root of Factor = = = = = = = = 9 19, = = 9 Problem Solving km km 3. 5 km 4. at most 226 km 5. C 6. F 7. D 8. G Reading Strategies between 9 and 10 Puzzles, Twisters & Teasers S. 6 R. 12 P. 10 T. 8 G. 5 I. 3 W. 2 H. 13 E. 9 U. 7 L. 11 P U L L T H E I R L E G S Product of Digital Roots of Factors 2 8 = = = = = = = = = = 9 Digital Root of Product = = = = = = = = = = 9

Name Date Class. Write in exponential form

Name Date Class. Write in exponential form Name Date Class Chapter 8 Practice 8-1 Exponents Write in exponential form. 1. 6 6 6 6 6 6 2. 7 7 7 7 3. ( 8) ( 8) ( 8) ( 8) 4. 5 5 5 b b b b Simplify. 5. 10 2 6. ( 6) 2 7. 8 2 8. ( 7) 2 9. ( 5) 3 10.