Beginning Algebra, 11th Edition

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 - ...

OBJECTIVE 3 Write radical expressions with quotients in lowest terms. Writing a Radical Quotient in Lowest Terms Write the quoti ...

35.Concept Check In Example 1(b),a student simplified by combining the and the to get , which is inco ...

Brain Busters Perform each operation and express the answer in simplest form. Solve each problem. 85.T ...

530 CHAPTER 8 Roots and Radicals Students of ...

Using the Squaring Property of Equality Solve Use the squaring property to square each side. On the left,. Subtract 1. CHECK Ori ...

Using the Squaring Property with a Radical on Each Side Solve Squaring property Subtract x. Divide by 8. CHECK Original equation ...

SECTION 8.6 Solving Equations with Radicals 533 Solving a Radical Equation Step 1 Isolate a radical.Arrange the terms so that a ...

The equation is quadratic because of the -term. To solve it, as shown in Section 6.5,we must write the equation in standard form ...

Using the Squaring Property Twice Solve Square each side. Subtract 9. Subtract x. Divide by 6. Square each side again. Apply the ...

(b) Cube each side. Apply the exponents. Standard form Factor. or Zero-factor property or Solve. CHECK Let Let ✓ True ✓ True Bot ...

Solve each equation. See Examples 5 and 6. 51.Concept Check Consider the ...

Solve each problem. Give answers to the nearest tenth. 73.To estimate the speed at which a car was traveling at the time of an a ...

SECTION 8.6 Solving Equations with Radicals 539 EXERCISES 79 – 84 FOR INDIVIDUAL OR GROUP WORK The most common formula for the a ...