Beginning Algebra, 11th Edition

Using the Quotient Rule to Simplify Radicals Use the quotient rule to simplify each radical. EXAMPLE 4 SECTION 8.2 Multiplying, ...

OBJECTIVE 4 Simplify radicals involving variables.Simplifying radicals with variable radicands, such as , can get a little trick ...

OBJECTIVE 5 Simplify other roots. The product and quotient rules for radicals also apply to other roots. SECTION 8.2 Multiplying ...

510 CHAPTER 8 Roots and Radicals (c) Factor; is a perfect cube. Product rule (d) Quotient rule = Take cube roots. NOW TRY y 5 = ...

Find each product and simplify. See Example 3. 55.Simplify the product in two ways. Fi ...

Simplify each radical. See Example 8. Simplify each radical. See Example 9. ...

SECTION 8.3 Adding and Subtracting Radicals 513 OBJECTIVES Adding and Subtracting Radicals 8.3 1 Add and subtract radicals. 2 Si ...

(c) Product rule Multiply. Add like radicals. (d) Product rule Multiply. Add like radicals. NOW TRY OBJECTIVE 3 Simplify more co ...

(d) Factor. Multiply. =m 234 Subtract like radicals. NOW TRY = 4 m 234 - 3 m 234 = 2 # 2 m 234 - 3 m 234 238 m^3 = 2 m; 2327 m^3 ...

Perform each indicated operation. Assume that all variables represent nonnegative real numbers. See Example 3. ...

SECTION 8.4 Rationalizing the Denominator 517 OBJECTIVES Rationalizing the Denominator 8.4 1 Rationalize denominators with squar ...

NOTE In Example 1(b),we could also have rationalized the original denominator, , by multiplying by since Either approach yields ...

Simplifying a Product of Radicals Simplify. Product rule Multiply fractions. Quotient rule Product rule Rationalize the denomina ...

OBJECTIVE 3 Rationalize denominators with cube roots. To rationalize a denominator with a cube root, we change the radicand in t ...

SECTION 8.4 Rationalizing the Denominator 521 Complete solution available on the Video Resources on DVD 8.4 EXERCISES Rationaliz ...

Simplify each radical. Assume that all variables represent positive real numbers. See Example 4. ...

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- 72 14 x+ 72 ...

OBJECTIVE 1 Simplify products of radical expressions. Multiplying Radical Expressions Find each product and simplify. (a) Subtra ...

(c) Square the binomial. = 25 - 102 x+x NOW TRY = 52 - (^2152) A 2 xB+ A 2 xB^2 A 5 - 2 xB 2 SECTION 8.5 More Simplifying and Op ...

Using Conjugates to Rationalize Denominators Simplify by rationalizing each denominator. Assume that (a) = Subtract. (^5) A 3 - ...