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Name________________________________ Math 3 5 6 7 Lesson 11.1 - Squares and Square Roots Goal: We will evaluate expressions using square roots. Vocabulary TERM DEFINITION Square of a number The number that you get when you multiply a number by _______________ Square Root The number that you multiply by _____________ to get the original number Perfect Squares Squares of __________ ____________ Radical Symbol The symbol used to show that you want to take the __________ _________ of a number. (The radical symbol acts as a grouping symbol!!!) Radicand The number or expression under the ____________ _____________ EXAMPLE Example 1- How do I use my calculator to square numbers and find square roots? Task Square a number Take the square root of a number What I put in my calculator... number, x², enter , number, enter Example 12² = 4.1² = -3² = (-7)² = √225 = √40.96 = √12 = Example 2- Perfect Squares - MEMORIZE!!! Use your calculator to find the following square roots: √1 = √4 = √49 = √64 = √9 = √16 = √81 = √100 = √121 = √25 = √36 = √169 = √196 = √225 = √144 = Example 3- Finding Square Roots Find the two square roots of the following numbers: 81 The two square roots of 81 could be ________ or ________ because ________________ = 81 and _________________ = 81. 36 The two square roots of 36 could be ______ or _______ because ________________ = 36 and _______________ = 36. Guided Practice Find the two square roots of the given number: 1. 25 2. 100 3. 144 4. 1 Example 4- Evaluating Square Roots When evaluating (finding the value of) a square root, we select the answer based on the sign to the ___________ of the radical symbol. √25 = 5 (Since there is not a sign on the left of the radical symbol, we assume the answer is positive) + √49 = _______ since the sign on the left is + - √9 = ______ since the sign on the left is √0 = ______ because ____________ = 0. √− 64 is ____________________ because _____________ =/ -64 and ____________ =/ -64 Guided Practice Evaluate the square root: 5. √81 = 8. + √121 = 6. - √81 = 9. √− 121 = 7. - √100 = Example 5- Solving Equations Involving Square Roots Solving Equations Review: To “undo” addition, we ___________________ . To “undo” subtraction, we ________________ . To “undo” multiplication, we ______________ . To “undo” division, we __________________ . NEW: To “undo” squaring a number, we _____________________________________________ . To “undo” taking the square root of a number, we ___________________ . Solve: x² = 121 X = ____________________ To solve for x, take the square root of both sides of The equation. Since we don’t know the sign of “x”, we write both solutions. X = _________ A shorter way to write the answer Solve: x² = 396 X = ____________________ To solve for x, take the square root of both sides of The equation. (You may have to round to the nearest tenth.) X = _________ A shorter way to write the answer Solve: ALWAYS “undo” addition/subtraction first!! x² + 20 = 101 X = __________ Guided Practice Solve: 10. x² = 144 11. x² = 114 12. x² + 30 = 130 13. x² - 25 = 50 Example 6- Application To solve for x, take the square root of both sides of The equation. Pam has enough flooring to cover 196 square feet. If she lays the flooring on a square area, what is the side length of the largest square she can make? Area of a square = s² A = s² Write an equation for the side length of a square. ________ = s² Substitute for the area of a square. √196 = √s² Since we are solving for “s” (side length), take the square root of Both sides of the equation. S = ______ or ________ But only one makes sense with this problem. Why? S = ______ Find the side length of the square if A = 39.69 m². (Use the formula A = s²) Guided Practice 12. Natalie is laying carpeting in her room. She has enough carpeting to cover 2500 square feet. If her room is a square area, what is the side length of one of the sides of the square?