Download 2.5 Square Roots Notes epc

Math 7 Learning Objective: 2.5: How to evaluate SQUARE ROOTS Name________________________ Block____ Date________________ Numbers such as 1, 4, 9, 16, and 25 are called __________________________, because they are squares of ___________________________. The symbol √ is called a ____________________________. POSITIVE SQUARE ROOTS What does square root mean? It means find the number that, when squared, produces the number inside the symbol. Examples: a) The square root of 16 is 4 because__________________________. b) The square root of 25 is 5 because__________________________. c) The square root of 9 is ____ because__________________________. d) The square root of 100 is _____ because__________________________. 
You try…Find each square root. Think…what times itself gives you 81? (? ∙ ? = 81) √81 =_____________________ √196 =_____________________ √49 =_____________________ √225 =_____________________ √121 =_____________________ √16 =_____________________ WE JUST LEARNED THAT every positive number has TWO square roots: _____________and ______________. NEGATIVE SQUARE ROOT (negative OUTSIDE the ) √25 represents the __________________ of the square root of 25. √25 represents both the _________________ and ______________ square root of 25. This means that √25 represents both _________and ___________. 
You try…Find each square root. √81 √196 √49 √121 SOLVING SQUARE ROOT EQUATIONS 2
A square and a square root cancel each other out. So to solve n² = 16, then: n = 16
c² = 9 c 2 = 
c = b² = 169 b2 = b = m² = 289 m2 = m = n2 = ± 16
n = ±4
 To place 25 chairs in a square arrangement, how many chairs should be in each row? ________  Moesha has 196 pepper plants that she wants to plant in square formation. How many pepper plants should she plant in each row? ___________  A new restaurant has ordered 64 tables for its outdoor patio. If the manager arranges the tables in a square formation, how many will be in each row? _____________  Area of a square is equal to the square of the length of a side. A = s² . A miniature portrait of George Washington is square and has an area of 169 square centimeters. How long is each side of the portrait? ______________  The formula for the perimeter of a square is P = 4s, where s is the length of a side. Find the perimeter of each square. Area = Area = Area = 324 square meters 49 square 144 square feet inches SQUARE ROOT of a NEGATIVE (negative INSIDE the ) What is √
? Think…what times itself gives you –25? (? ∙ ? = –25) ___________________________ Find each square root. 2. √9 3. √ 36 4. √196 1. √16 5. √121 6. √ 81 7. √4 8. √289 Solve each equation d² = 64 x² = 121 n² = 169 WHAT IF IT IS NOT A PERFECT SQUARE? The square root of a number that is not a perfect square falls between two _______________ whole numbers. Step 1 Determine whether a number is a perfect square. 1. Is the number 29 a perfect square? Is there a whole number which can be squared to equal 29? _____ Step 2 Find the two consecutive whole numbers between which the √
lies. 2. The number 25 is the closest perfect square _________ than 29. What is √25? _____ 3. The number 36 is closest perfect square greater than 29. What is √36? _____ 4. √29 lies between √25 and √36 . What are the two consecutive whole numbers between which √29 lies? _____________ Find the two consecutive whole numbers between which the square root of a given number lies. Then circle the nearest integer. √19 _______ _______ √57 _______ _______ √48 _______ _______ √99 _______ _______ √17 _______ _______ √2 _______ _______ ***Under what condition is √ > √25 ? Spiral Review
1) The radius of the Sun is 6.96 10 meters. Write this distance in standard form. __________________ Write each expression using exponents 2) 6 ∙ 6 ∙ 6 3) 2 ∙ 3 ∙ 3 ∙ 2 ∙ 2 ∙ 2 4) 5) What is absolute value of ‐18? 6) Find 7) 8 – 2(5) = 8) (–2)(3)(–5) = Using the numbers 2, 3, and 4, write an example of the 9) Associative Property of Multiplication ________________ ; 10) Distributive Property ________________