Blitzer - College Algebra 8th Edition

Ch. P - Fundamental Concepts of Algebra

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Blitzer 8th Edition

Ch. P - Fundamental Concepts of Algebra

Section P.3

Problem 10

Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √144+√25

Problem 12

Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. $\sqrt{(- 17)^{2}}$

Problem 14

Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. √27

Problem 16

Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. $the square root of 125 x squared$

Problem 18

Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. $\sqrt{10 x} \cdot \sqrt{8 x}$

Problem 21

Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. $\sqrt{2 x^{2}} \cdot \sqrt{6 x}$

Problem 22

Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. $\sqrt{6 x} \cdot \sqrt{3 x^{2}}$

Problem 24

Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. $\sqrt{\frac{1}{49}}$

Problem 29

Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. $\frac{\sqrt{150 x^{4}}}{\sqrt{3 x}}$

Problem 34

In Exercises 33–44, add or subtract terms whenever possible. 8√5+11√5

Problem 43

Add or subtract terms whenever possible. $3\sqrt{8} - \sqrt{32} + 3\sqrt{72} - \sqrt{75}$

Problem 45

Rationalize the denominator.

$\frac{1}{\sqrt7}$

Problem 47

Rationalize the denominator.

$\frac{\sqrt{2}}{\sqrt{5}}$

Problem 48

Evaluate each expression or indicate that the root is not a real number.

$\frac{\sqrt7}{\sqrt3}$

Problem 50

Rationalize the denominator.

$\frac{3}{3+\sqrt7}$

Problem 51

Rationalize the denominator. $\frac{7}{\sqrt{5} - 2}$

Problem 52

Rationalize the denominator.

$\frac{5}{\sqrt3-1}$

Problem 53

Rationalize the denominator.

$\frac{6}{\sqrt5+\sqrt3}$

Problem 54

Rationalize the denominator. $\frac{11}{\sqrt{7} - \sqrt{3}}$

Problem 56

Evaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ³√8

Problem 59

Evaluate each expression in Exercises 55–66, or indicate that the root is not a real number. $\sqrt[4]{- 16}$

Problem 66

Evaluate each expression in Exercises 55–66, or indicate that the root is not a real number. $\sqrt[6]{\frac{1}{64}}$

Problem 75

Add or subtract terms whenever possible. $4\sqrt[5]{2} + 3\sqrt[5]{2}$

Problem 82

Add or subtract terms whenever possible. √3+³√15

Problem 83

Evaluate each expression without using a calculator. 36^1/2

Problem 86

Evaluate each expression without using a calculator. 27^1/3

Problem 90

Evaluate each expression without using a calculator. 16^-6/2

Problem 93

Simplify using properties of exponents. $\frac{20x^{\frac{1}{2}}}{5x^{\frac{1}{4}}}$

Problem 95

Simplify using properties of exponents. $(x^{\frac{2}{3}})^{3}$

Problem 102

Simplify by reducing the index of the radical. $the fourth root of 7 squared$