Download Rational Exponents/Solving Radical Equations 7.4 notes

H. Algebra 2
7.4 - 7.5 notes: Rational Exponents/Solving Radical Equations
7.4 notes:
Another way to write a radical expression is to use a rational exponent.
Examples:
√
√
√
√
√
√
√
Example: Simplifying Expressions with Rational Exponents
a.
d.
(
)
b.
c.
e.
f.
Rational Exponents:
If the nth root of a is a real number and m is an integer:
√
a.
√
b.
√
c.
√
Example: Converting to and From Radical Form
a. Write the following exponential expressions in radical form:
( )
(
b. Write the following radicals in exponential form:
√
√
√
√
Example: Simplifying Numbers with Rational Exponents
a.
d.
b.
(
√
√
)
e.
c.
√
√
f.
)
Example: Writing an Expression in Simplest Form
a.
b.
7.5 notes:
Radical Equations have a variable in the radicand (under the root) or can be rewritten with a rational exponent.
Solve:
2  3x  2  6
How can I determine if the solutions will be real or extraneous?
Solve:
2 3  x  2   98
2
Solve:
x 3 5  x
Solve:
x  2x  2
Solve:
 2 x  1
0.5
  3x  4 
Solve:
x  25  x  5
0.25
0