Intermediate Algebra (11th edition)

(d) The greatest perfect cubethat divides into 16 is 8, so factor 16 as 8 is a perfect cube. Product rule = 2232 238 = 2 = 238 # ...

NOTE From Example 5,we see that if a variable is raised to a power with an expo- nent divisible by 2, it is a perfect square. If ...

In Section 9.1we will see that an equation such as has two solutions: (the principal, or positive, square root of 7) and Similar ...

By the Pythagorean theorem, the square of the length of the hypotenuse dof the right triangle in FIGURE 8is equal to the sum of ...

= 282 Leave in radical form. NOW TRY = 292 + 1 - 122 = 236 - 1 - 3242 + 14 - 522 x 2 =6,y 2 =4,x 1 =3,y 1 = 5 d= 21 x 2 - x 122 ...

Express each radical in simplified form. Assume that all variables represent positive real numbers. See Example 5. ...

Find the perimeter of each triangle. Hint: For Exercise 125, use Solve each problem. 127.The following letter appeared i ...

132.The illumination I, in foot-candles, produced by a light source is related to the distance d, in feet, from the light source ...

Adding and Subtracting Radicals Add or subtract to simplify each radical expression. (a) Product rule Multiply. (b) Product rule ...

(c) Factor. Product rule The radicands are both x, but since the indexes are different, this expression cannot be simplified fur ...

456 CHAPTER 8 Roots, Radicals, and Root Functions Complete solution available on the Video Resources on DVD 8.4 EXERCISES Simpli ...

55.Concept Check Which sum could be simplified without first simplifying the individual radical expressions? A. B. C. D. 56.Conc ...

Multiplying Binomials Involving Radical Expressions Multiply, using the FOIL method. (a) First Outer Inner Last = 230 + 25 + 326 ...

(f ) Difference of squares and NOW TRY NOTEIn Example 1(d),we could have used the formula for the square of a binomial to obtain ...

(b) (c) Less work is involved if we simplify the radical in the denominator first. Now we rationalize the denominator. NOW TRY R ...

from page 460 Multiply. = Multiply. 3234 4 =^3234238 = 2 2 # 2 = 3234 2238 = 3 # 234 2232 # 234 3 2232 B^32716 = 3 2232 SECTION ...

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. ...