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Do Now: Solve the following equations: x 2 = 25 x 2 = 50 Explain your thinking.

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Solving Quadratic Equations by Finding Square Roots March 5, 2015

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Square Root of a Number If b 2 = a, then b is the square root of a. Example: If 3 2 = 9, then 3 is the square root of 9.

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VocabularyV All positive real numbers have 2 square roots – Positive square root – principle square root Negative square root Square roots are written with a radical symbol √ Radicand – number inside the radical symbol

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Radical Radicand Radical Sign

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Positive or Negative To indicate that we want both the positive and the negative square root of a radicand we put the symbol ± (read as plus minus) in front of the root.

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What about zero? Zero has one square root which is 0. Negative numbers don't have real square roots since a square is either positive or 0. The square roots of negative numbers are imaginary numbers. Example : √-9

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A negative outside the Radicand A negative sign outside the radicand symbolizes the inverse of the square root. Example: -√9 = -3

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Evaluate the expression 1.√64 2.-√64 3.√0 4.±√0.25 5.√-4

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Which of the following are not perfect squares? a.-√121 b.-√1.44 c.√0.09 d.√7 √7 is the only irrational number

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Radical Expressions The square root symbol is a grouping symbol. Evaluate √b 2 -4ac when a=1, b=-2, and c=-3

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Solving x 2 = d If d > 0, then x 2 = d has 2 solution: + and – If d = 0, then x 2 = d has 1 solution: 0 If d < 0, then x 2 = d has no real solution.

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Solve each equation 1.x 2 = 2 2.x 2 = 5 3.x 2 = -1

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Rewriting before finding square roots 3x 2 – 48 = 0 3x 2 = 48 X 2 = 16 X = ± √16 X = ±4

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Falling Objects Model h = -16t 2 + s h is height in feet t is time in seconds s is the initial height the object was dropped

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Solve the Equation If an object is dropped from an initial height 48 feet, how long will it take to reach the ground? h = -16t 2 + s 0 = -16t 2 + 48 -48 = -16t 2 3 = t 2 About 1.7 seconds = t

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Properties of Square Rootsp Product Property – Example: Quotient Property -

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Examples 1. √500 2.

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Rationalizing the Denominator You CANNOT leave a radical in the denominator of a fraction! (the numerator is OK) Just multiply the top & bottom of the fraction by the radical to “rationalize” the denominator.

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An Example

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Try these on your own Solve. 3 - 5x 2 = -9 3(x-2) 2 =21

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