Find each product. See Sections 5.5 and 5.6.
- 1 p+q 21 a-m 2 94. 13 w- 822
16 x- 1216 x+ 12 1 r+ 721 r- 7214 x+ 7218 x- 32 ab 13 a^2 b- 2 ab^2 + 72PREVIEW EXERCISES
SECTION 8.5 More Simplifying and Operations with Radicals 523OBJECTIVESMore Simplifying and Operations with Radicals
8.5
1 Simplify products of
radical expressions.
2 Use conjugates to
rationalize
denominators of
radical expressions.
3 Write radical
expressions with
quotients in lowest
terms.
A set of guidelines to use when you are simplifying radical expressions follows.Guidelines for Simplifying Radical Expressions- If a radical represents a rational number, use that rational number in place of
the radical.
Examples:- If a radical expression contains products of radicals, use the product rule for
radicals, to get a single radical.
Examples:- If a radicand of a square root radical has a factor that is a perfect square,
express the radical as the product of the positive square root of the perfect
square and the remaining radical factor. A similar statement applies to higher
roots.
Examples:- If a radical expression contains sums or differences of radicals, use the
distributive property to combine like radicals.
Examples:.cannot be simplified further.- Rationalize any denominator containing a radical.
Examples:B
3
1
4
=
231
234
=
231 # 232
234 # 232=
232
238
=
232
2
5
23
=
5 # 23
23 # 23=
523
3
322 + 423
322 + 422 can be combined to get 7 222316 = 238 # 2 = 238 # 232 = 2232
220 = 24 # 5 = 24 # 25 = 225
25 # 2 x= 25 x, 233 # 232 = 236
n
2 a#
n
2 b
n
2 ab,