Intermediate Algebra (11th edition)

(c)

Factor.

Product rule

The radicands are both x, but since the indexes are different, this expression cannot

be simplified further.

= 10 x 2 x+ 12 x 23 x

= 5 # 2 x 2 x+ 3 # 4 x 23 x

= 524 x^2 # 2 x+ 32364 x^3 # 23 x

= 524 x^2 #x+ 32364 x^3 #x

524 x^3 + 32364 x^4

SECTION 8.4 Adding and Subtracting Radical Expressions 455

NOW TRY

Adding and Subtracting Radicals with Fractions

Perform the indicated operations. Assume that all variables represent positive real

numbers.

(a)

Quotient rule; factor.

Product rule; find the square roots.

Multiply;.

Write with a common denominator.

(b)

Quotient rule

Simplify denominators.

Write with a common denominator.

= Subtract fractions. NOW TRY

10 x 235 - 3234

x^3

=

10235 #x

x^2 #x

-

3234

x^3

=

10235

x^2

-

3234

x^3

= 10

235

23 x^6

- 3

234

23 x^9

10

B

3

5

x^6

- 3

B

3

4

x^9

a

c+

b

c=

a+b

= c

523 + 4

2

=

523

2

+

4

2

(^22) = 1
22

=

523

2

+ 2

= 2 ¢

523

4

≤ + 4 ¢

222

422

≤

= 2

225 # 3

216

+ 4

24 # 2

216 # 2

2

B

75

16

+ 4

28

232

EXAMPLE 3

Be careful. The

indexes are

different.

Keep track of

the indexes.

NOW TRY
EXERCISE 2
Add or subtract to simplify
each radical expression.
Assume that all variables
represent positive real
numbers.

(a)

(b)

(c) 23128 t^4 - 2272 t^3

524 a^5 b^3 + 2481 ab^7

3232000 - 423128

NOW TRY ANSWERS

2. (a)
   (b)
   (c)


3. (a)

(b)

12232 + 7 x 239

x^4

5 - 827

3

4 t 232 t- 12 t 22 t

15 a+ 3 b 224 ab^3

14232

NOW TRY
EXERCISE 3
Perform the indicated
operations. Assume that all
variables represent positive
real numbers.

(a)

(b) 6
B

3

16

x^12

+ 7

B

3

9

x^9

5

25

245

- 4

B

28

9