Intermediate Algebra (11th edition)

Adding and Subtracting Radicals

Add or subtract to simplify each radical expression.

(a)

Product rule

Multiply.

(b)

Product rule

Multiply.

Combine like terms.

(c) The radicands differ and are already simplified, so

cannot be simplified further.

223 - 425 223 - 425

= 25 x

= 425 x- 325 x

= 2 # 225 x- 325 x 24 =2; 29 = 3

= 224 # 25 x- 29 # 25 x

2220 x- 245 x, xÚ 0

= 926 626 + 326 = 16 + 3226

= 626 + 326

= 3 # 226 + 326 24 =2; 29 = 3

= 324 # 26 + 29 # 26

3224 + 254

EXAMPLE 1

454 CHAPTER 8 Roots, Radicals, and Root Functions

NOW TRY

CAUTION The root of a sum does not equal the sum of the roots.For example,

since 29 + 16 = 225 = 5, but 29 + 216 = 3 + 4 =7.

29 + 16 Z 29 + 216

CAUTION Only radical expressions with the same index and the same radi-

cand may be combined.

NOW TRY
EXERCISE 1
Add or subtract to simplify
each radical expression.

(a)

(b)

(c) 627 - 223

• 263 t+ 3228 t, tÚ 0

212 + 275

NOW TRY ANSWERS

1. (a) (b)
   (c)The expression cannot
   be simplified further.

723 327 t

Adding and Subtracting Radicals with Higher Indexes

Add or subtract to simplify each radical expression. Assume that all variables repre-

sent positive real numbers.

(a)

Factor.

Product rule

Find the cube roots.

Multiply.

Distributive property

Combine like terms.

(b)

Factor.

Product rule

Find the cube root.

= 12 + 2 xy 223 x^2 y Distributive property

= 223 x^2 y+ 2 xy 23 x^2 y

= 223 x^2 y+ 238 x^3 y^3 # 23 x^2 y

= 223 x^2 y+ 2318 x^3 y^32 x^2 y

223 x^2 y+ 238 x^5 y^4

=- 11232

= 14 - 152232

= 4232 - 15232

= 2 # 2 # 232 - 5 # 3 # 232

= 2238 # 232 - 52327 # 232

= 2238 # 2 - 52327 # 2

22316 - 52354

EXAMPLE 2

Remember to write the

index with each radical.

This result cannot

be simplified

further.