Beginning Algebra, 11th Edition

Finding Cube Roots Find each cube root. (a) What number can be cubed to give 8? Because (b) , because (c) because. NOW TRY Notic ...

Find each square root. See Examples 2 and 4(c). Find the square of each radi ...

Solve each problem. Give any decimal approximations to the nearest tenth. See Example 7. 502 CHAPTER 8 Roots and Radicals 25 cm ...

One of the many proofs of the Pythagorean theorem was given in the Connections boxin this section. Two more are given in Exercis ...

93.Concept Check To help find cube roots, complete this list of perfect cubes. 94.Concept Check To help find fourth roots, compl ...

Using the Product Rule to Multiply Radicals Use the product rule for radicals to find each product. EXAMPLE 1 SECTION 8.2 Multip ...

Multiplying and Simplifying Radicals Find each product and simplify. (a) Factor; 25 is a perfect square. Product rule Multiply. ...

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 ...