Download Intermediate Algebra Section 7.3 – Simplifying Radical Expressions

Intermediate Algebra
Section 7.3 – Simplifying Radical Expressions
Notice that 9 ⋅ 4 = 3⋅ 2 = 6 and 9 ⋅ 4 = 36 = 6 . This implies
that 9 ⋅ 4 = 9 ⋅ 4 . This illustrates the product rule for radicals.
Product Property for Radicals
If a and n b are real numbers, then
Example:
n
a ⋅ n b = n ab
Use the Product Property to simplify.
11 ⋅ 10
a)
b)
We have a similar rule for quotients. Notice
which implies
3
10 ⋅ 3 5
4 2
= and
9 3
4 2
= ,
9 3
4
4
=
.
9
9
Quotient Property for Radicals
If
n
a and
n
b are real numbers and
n
b is not zero, then
n
a na
.
=
b nb
Section 7.3 – Simplifying Radical Expressions
Example:
a)
4
Use the Quotient Property to simplify.
16y
81x 4
y10
6
9x
b)
Sometimes we use the reverse of the rule to simplify.
Example:
a)
27
b)
9x 5 y 7
c)
4
162m6
Simplify. Assume that all variables can be any real
number.
page 2
Section 7.3 – Simplifying Radical Expressions
d)
3
40y10
Example:
Simplify. Assume that all variables are greater than or
equal to zero.
125x 2
a)
b)
3
−81a 4b5
c)
5
32z
Example:
a)
page 3
12
Simplify. Assume that all variables are greater than or
equal to zero.
6 ⋅ 21
Section 7.3 – Simplifying Radical Expressions
8 x3 ⋅ 6 x
b)
c)
2 12 xy 3 ⋅ 3 30 x 2 y
Example:
48a 5
3a
a)
3
b)
128x 3
3
2x
Example:
a)
Simplify. Assume that all variables are greater than
zero.
237
Simplify.
page 4
Section 7.3 – Simplifying Radical Expressions
b)
4
page 5
9 ⋅ 6 12
Example:
The radius r of a sphere whose volume V is given by
3V
r=3
.
4π
a) Write the radius of a sphere whose volume is 9 cubic centimeter
as a radical in simplified form.
b) Write the radius of a sphere whose volume is 32π cubic
centimeters as a radical in simplified form.