Intermediate Algebra (11th edition)

Rationalizing Binomial Denominators Rationalize each denominator. (a) =- 3 A 1 - 22 B, or - 3 + 322 Distributive property = 3 - ...

OBJECTIVE 4 Write radical quotients in lowest terms. Writing Radical Quotients in Lowest Terms Write each quotient in lowest ter ...

464 CHAPTER 8 Roots, Radicals, and Root Functions Complete solution available on the Video Resources on DVD 8.5 EXERCISES Concep ...

Rationalize the denominator in each expression. Assume that all variables represent positive real numbers. See Examples 2 and 3. ...

Brain Busters Rationalize each denominator. Assume that all radicals represent real num- bers and no denominators are 0. ...

SUMMARY EXERCISES on Operations with Radicals and Rational Exponents 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22 ...

468 CHAPTER 8 Roots, Radicals, and Root Functions OBJECTIVES An equation that includes one or more radical expressions with a va ...

Using the Power Rule Solve Step 1 25 x- 1 =- 3 25 x- 1 + 3 = 0. EXAMPLE 2 SECTION 8.6 Solving Equations with Radicals 469 Solvin ...

Step 3 The new equation is quadratic, so write it in standard form. Equation from Step 2 Subtract 4. Add x. Factor. or Zero-fact ...

SECTION 8.6 Solving Equations with Radicals 471 The equation still contains a radical, so isolate the radical term on the right ...

OBJECTIVE 4 Use the power rule to solve a formula for a specified variable. Solving a Formula from Electronics for a Variable An ...

SECTION 8.6 Solving Equations with Radicals 473 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35.Conce ...

Solve each formula for the indicated variable. See Example 7.(Source:Cooke, Nelson M., and Joseph B. Orleans, Mathematics Essent ...

We can use this definition to define any square root of a negative real number. SECTION 8.7 Complex Numbers 475 For any positive ...

Dividing Square Roots of Negative Numbers Divide. (a) Quotient rule Divide. = 5 = 225 = B 75 3 = i 275 i 23 2 - 75 2 - 3 EXAMPLE ...

OBJECTIVE 3 Add and subtract complex numbers.The commutative, asso- ciative, and distributive properties for real numbers are al ...

(c) FOIL Multiply. = 17 - 7 i = 2 - 7 i+ 15 = 2 - 7 i- 151 - 12 = 2 - 10 i+ 3 i- 15 i^2 = 2112 + 21 - 5 i 2 + 3 i 112 + 3 i 1 - ...

Substitute for = 1 - i = - i+ 1 1 = - 1 i^2. - i- 1 - 12 - 1 - 12 SECTION 8.7 Complex Numbers 479 (b) = Distributive property; m ...

Multiply or divide as indicated. See Examples 2 and 3. 19. 20. 21. 22. 23. 24. 25. 26. 27.Every real number is a ...

Find each power of i. See Example 8. 85.A student simplified as follows: Explain the mathe ...