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## 9.1 Square Roots

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**9.1 Square Roots**Pre-Algebra**Vocabulary**• Square root: If , then m is the square root of n. • Radical sign: represents the positive square root. represents the negative square root. • Perfect square: Any number that has an integer square roots. • Example: ,**Perfect Squares**These are perfect squares. They have the same length and the same width. Area = length ∙ width**Example 1: Finding Square Roots**• What are the square roots of 81? • 92=81 and (-9)2=81. • The square roots of 81 are 9 and -9. • What are the square roots of 49?**Example 2: Evaluating Square Roots**Why? When computing the square root with the radical sign, you will have only one answer-the positive square root**Example 3: Solving a Square Root Equation**• To find the minimum speed a pole vaulter must run, you must use the following equation s = 8 • S is the pole vaulter’s speed in feet per second,and h is the height vaulted in feet. • If the pole vaulter vaults over a height of 25 feet, find the pole vaulter’s minimum speed. Write equation for speed of apole vaulter. Substitute 25 for h. Evaluate square root. Multiply.**Example 5: Solving Equations Using Square Roots**• Solve the equation. When solving for a variable, you will have two answers-the positive and negative square root. a.x2= 25 x2= 25 Write original equation. Use definition of square root. Evaluate square root.**Example 5: Solving Equations Using Square Roots**• Solve the equation. b.h2+ 5 = 54 h2+ 5 = 54 Write original equation. Undo the addition of 5. Simplify. Use definition of square root. Evaluate square root.**You Try!**• Solve the equation. 1. 2. x2= 81 x2= 1 x = ±9 x = ±1**12x2= 108**x = ±3 x2– 5 = – 1 x = ±2 3. 4.**Think about it!!**Can you find ? Why or Why not?