Beginning Algebra, 11th Edition

Multiplying and Simplifying Radicals

Find each product and simplify.

(a)

Factor; 25 is a perfect square.

Product rule

Multiply.

We could have used the product rule to get and then simpli-

fied. However, the product rule as used here allows us to obtain the final answer with-

out using a large number like 675.

(b)

Product rule

Factor; 4 is a perfect square.

Product rule

; Multiply.

Multiply.

(c)

Commutative property; product rule

Multiply.

Factor; 9 is a perfect square.

Product rule

Multiply. NOW TRY

NOTE We could also simplify the product in Example 3(b)as follows.

Factor.

Product rule

Commutative property

Same result Multiply.

There is often more than one way to find such a product.

= 426

= 2 # 2 # 22 # 23

= 222 # 223 24 = 2

= 24 # 22 # 24 # 23

= 24 # 2 # 24 # 3

28 # 212

= 1822

= 6 # 3 # 22 29 = 3

= 629 # 22

= 629 # 2

= 6218

= 2 # 3 # 23 # 6

223 # 326

= 426

= 2 # 2 # 26 24 = 2

= 24 # 24 # 22 # 3

= 24 # 2 # 4 # 3

= 28 # 12

28 # 212

29 # 275 = 2675

= 1523

= 3 # 523 225 = 5

= 3225 # 23

= 3225 # 3

= 3275 29 = 3

29 # 275

EXAMPLE 3

506 CHAPTER 8 Roots and Radicals

NOW TRY
EXERCISE 3
Find each product and
simplify.

(a)

(b) 26 # 230

216 # 250

NOW TRY ANSWERS

3. (a) 2022 (b) 625

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