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?