4.5 “Square Roots”Product Property: = ·

= · = 3

Quotient Property: =

= =

Examples:

More Examples

4. ·

5. 3· 2

Rationalizing the DenominatorSimplify the following: Remember…you cannot have a radical sign in the denominator of your final answer!!!!

10.

11. **If there is a binomial in the denominator, multiply by the conjugate (opposite sign)**

Rationalizing Examples12.

13.

14.

15.

Rationalizing Examples with Conjugates16.

17.

18.

19.

Solve a Quadratic EquationSolve the following:

20. 3x2 + 5 = 41

Steps:

1. Isolate the squared term

2. Take the square root of each side

3. Simplify the radical

4. Answer should be ±

Solving Quadratic Equation Examples21. 5x2 = 80

22. z2 – 7 = 29

23. 3(x – 2)2 = 72

Word ProblemsWhen an object is dropped, its height (in feet) above the ground after t seconds can be modeled by the function… h = -16t2 + h0

h0 = initial height (in feet)

t = time (in seconds)

For a science project, students must design a container that prevents an egg from breaking when dropped from 50 feet. How long does it take it to hit the ground?