Solving Quadratic Equations by Finding Square Roots

Square Roots

• Square roots: a number that produces a specified quantity when multiplied by itself.– Example: = 7 (7 × 7 = 49)

• Types of square roots:– Positive: = 9– Negative: = -10– Zero Square Root: = 0– Two square roots: = – Undefined: (no square root)

Perfect Squares

• Perfect Squares: numbers whose square roots are integers.

12 1

22 4

32 9

42 16

52 25

62 36

72 49

82 6492 81102 100112 121122 144132 169142 196152 225

Not Perfect Squares

• Numbers that are not perfect squares must be written using the radical symbol or approximated. These numbers are irrational.–Irrational Numbers: numbers that

cannot be written as fractions–Examples: or

Evaluating Square Roots

Evaluating a Radical Expression

When a = 1, b = -2 and c = -3, evaluate:

Evaluating a Radical Expression

When a = 2, b = 4

Falling Object ModelFormula:

h = ground levelt = times = initial height

h=−16 𝑡 2+s• An engineering student is in an “egg dropping

contest.” The goal is to create a container for an egg so it can be dropped from a height of 32 feet without breaking the egg. To the nearest tenth of a second, about how long will it take for the egg’s container to hit the ground. Assume there is no air resistance. (h = 0 when it hits the ground)

h=−16 𝑡 2+s• An engineering student is in an “egg dropping

contest.” The goal is to create a container for an egg so it can be dropped from a height of 64 feet without breaking the egg. To the nearest tenth of a second, about how long will it take for the egg’s container to hit the ground. Assume there is no air resistance.

HomeworkPage: 507

8-20 evens and 36, 38.