Transcript solving by square roots

Do Now:
Solve the following equations:
x2 = 25
x2 = 50
Explain your thinking
.
Solving Quadratic Equations
by Finding Square Roots
March 5, 2015
Square Root of a Number
If b2 = a, then b is the square root of a.
Example: If 32 = 9, then 3 is the square root of 9.
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
Radical
Radicand
Radical Sign
3
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.
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
A negative outside the
Radicand
A negative sign outside the radicand
symbolizes the inverse of the square root.
Example: -√9 = -3
Evaluate the expression
1. √64
2. -√64
3. √0
4. ±√0.25
5. √-4
Which of the following are not
perfect squares?
a. -√121
b. -√1.44
c. √0.09
d. √7
√7 is the only irrational number
Radical Expressions
The square root symbol is a grouping symbol.
Evaluate √b2 -4ac when a=1, b=-2, and c=-3
Solving x2 = d
If d > 0, then x2 = d has 2 solution: + and –
If d = 0, then x2 = d has 1 solution: 0
If d < 0, then x2 = d has no real solution.
Solve each equation
1. x2 = 2
2. x2 = 5
3. x2 = -1
Rewriting before finding square roots
3x2 – 48 = 0
3x2 = 48
X2 = 16
X = ± √16
X = ±4
Falling Objects Model
h = -16t2 + s
h is height in feet
t is time in seconds
s is the initial height the object was dropped
Solve the Equation
If an object is dropped from an initial height 48 feet, how
long will it take to reach the ground?
h = -16t2 + s
0 = -16t2 + 48
-48 = -16t2
3 = t2
About 1.7 seconds = t
Properties of Square Rootsp
Product Property –
Example:
ab  a * b
40  4 *10  4 * 10  2 10
Quotient Property -
a
a

b
b
3
3
3


4
2
4
Examples
1. √500
2.
25
9
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.
An Example
25
3
25

3

5 * 3
3 * 3

5 3
9

5 3
3
Try these on your own
Solve.
• 3 - 5x2 = -9
• 3(x-2)2=21