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WARM UP

WARM UP. 3. SKILL CHECK Evaluate the expression 3x 2 – 108 when x = -4. Find an ordered pair s olution to the equation 3x + 4y = 12. WARM UP. 2. SKILL CHECK Evaluate the expression 3x 2 – 108 when x = -4. Find an ordered pair solution to the equation 3x + 4y = 12. WARM UP. 1.

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WARM UP

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  1. WARM UP 3 SKILL CHECK Evaluate the expression 3x2 – 108 when x = -4. Find an ordered pair solution to the equation 3x + 4y = 12

  2. WARM UP 2 SKILL CHECK Evaluate the expression 3x2 – 108 when x = -4. Find an ordered pair solution to the equation 3x + 4y = 12

  3. WARM UP 1 SKILL CHECK Evaluate the expression 3x2 – 108 when x = -4. Find an ordered pair solution to the equation 3x + 4y = 12

  4. WARM UP 0 SKILL CHECK Evaluate the expression 3x2 – 108 when x = -4. Find an ordered pair solution to the equation 3x + 4y = 12

  5. 9.1 Square Roots GOAL Evaluate and approximate square roots. KEY WORDS Square root Positive square root Negative square root Radicand Perfect square Radical expression

  6. 9.1 Square Roots You already know how to find the square of a number. For instance the square of 3 is: 32 = 9 The square of -3 is also 9. [(-3)2 = 9] In this lesson you will learn about the inverse operation of finding a square root of a number.

  7. 9.1 Square Roots SQUARE ROOT OF A NUMBER If b2 = a, then b is a square root of a. Examples:32= 9, so 3 is a square root of 9. (-3)2= 9, so -3 is a square root of 9.

  8. 9.1 Square Roots All positive real numbers have two square roots: a positive square root (or principal square root) and a negative square root. Square roots are written with a radical symbol . The number or expression inside a radical symbol is the radicand. In the following example, 9 is the radicand. As shown in part (a), the radical symbol indicates the positive square root of a positive number.

  9. 9.1 Square Roots EXAMPLE 1Write the equation in words. a) = 3 b) - = -3 b) ± = ±3 SOLUTION EQUATION WORDS = 3 The positive square root of 9 is 3. - = -3 The negative square root of 9 is -3. ± = ±3The positive and negative square roots of 9 are 3 and -3.

  10. 9.1 Square Roots NUMBER OF SQUARE ROOTS Positive real numbers have two square roots. Zero has only one square root: zero. Negative numbers do not have real square roots because the square of every number is either positive or zero.

  11. 9.1 Square Roots EXAMPLE 2Find Square Roots of Numbers. a) b) - c) ± d) SOLUTION = = 8 Positive Square Root. - = -= -8 Negative Square Root. ± = ± = ± 8 Two Square Roots. = 0 Square Root of Zero is Zero.

  12. 9.1 Square Roots PERFECT SQUARES The square of an integer is called a perfect square. A square root of a perfect square is an integer. If n is a positive number that is not a perfect square, then it can be shown that is an irrational number. An irrational number is a number that is not the quotient of integers.

  13. 9.1 Square Roots PERFECT SQUARES = 2 4 is a perfect square is an integer. ≈ 1.4142 is not a perfect square is neither an integer nor a rational number.

  14. 9.1 Square Roots EXAMPLE 3Evaluate Square Roots of Numbers. Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth. a) - b) SOLUTION - = - = -7 ≈ 1.73

  15. 9.1 Square Roots RADICAL EXPRESSIONS An expression written with a radical symbol is called a radical expression, or sometimes just a radical.

  16. 9.1 Square Roots EXAMPLE 4Evaluate a Radical Expression. Evaluate when a = 1, b = -2, and c = -3. SOLUTION The radical symbol is a grouping symbol. You must evaluate the expression inside the radical symbol before you find the square root. = Substitute values for a, b, and c. = Simplify. = Add. = 4 Find the positive square root.

  17. 9.1 Square Roots YOUR TURN Textbook pages 502and 503 #s 25-40and 53-74

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