Download Solving Radical Equations

Solving Radical
Equations
Section 12.3
July 6, 2017
Warm Up
1. Simplify ( 6 )
2
2. Solve
x 4
3. Solve
x  17
4. Solve x  5x  6  0
2
10
x
5. Solve

2x + 4 x +2
Goals
► Solve
a radical equation
► California State Standard 2:
Understand and use such operations as
taking the opposite, finding the
reciprocal, taking a root, and raising to a
fractional power. They understand and
use the rules of exponents.
Key Terms
► Radical—a
square root
► Extraneous solution—a trial solution that
does not satisfy the original equation
Squaring both sides of an equation
►If
a = b, then a2 = b2, where a
and b are algebraic
expressions.
Example
x  1  5, so x  1  25
Example 1
a. Solve
x -10 = 0
b. Solve 8 x -3 =16
c. Solve
x -6 = 4
Example 2
Solve
3x +1  16
Solve
x - 4 + 5 = 11
Solve
3n +1 -3 = 1
Example 3
Solve
4x -3  x and
check for extraneous solutions
Example 4
► Solve
the equation and check for
extraneous solutions
1.
x +6 = x
2. x = 8 -2x
3.
n +4 =0
Example 5
► The
horizontal distance S (in meters)
traveled by a projectile is related to its
initial velocity (in m/sec) by the formula
v 
S
0.03
If v = 224 m/sec, find S.
Key Terms
► Cube
root of a—If b3 =a, then b is called
the cube root of a.
► Radical notation—the nth root of a is
written as n a
► Rational exponent—when you have a
fraction in the exponent
Rational Exponents
► Let
a be a nonnegative number, and let m
and n be positive integers
a
m
n
 (a )  ( a )
1
n
m
n
m
Example 1
► Find
root
the following cube root or square
a. 125
b.
3
1
3
125
c. 81
f. 64
3
2
g. ( 4 )
1
2
d. 216
e. ( 27 )
3
1
3
5
2
Example 2
► Rewrite
the following expressions using
rational exponent notation and radical
notation.
a. 25
3
b. 27
4
c. 16
d. 8
4
3
3
2
3
2
Properties of Rational Exponents
► Let
a and b be nonnegative real numbers
and let m and n be rational numbers.
am •an = am+n
(am)n = amn
(ab)m = ambm
Example 3
► Evaluate
the expression using the
properties fractional exponents
a. 6  6
4
3
b. (3 )
1
2
2
3
4
c. (36  49)
1
2
Example 4
► Simplify
the variable expression using the
properties of rational exponents
a. ( x  y )
1
3
6
b. (x  y ) x
4
1
2
c. (x  x )
5
1
3
d.
3
3
1
2
x (x  y )
3
2
1
3
Homework
► Page
707 (4 – 32 even)
► Page 709 (5 - 13)
► Page 713 (10 - 44 even)