Exam 8: Radical Expressions and Equations

Solve the problem. -The cost of manufacturing clocks is given by $c=81 \sqrt{n+49}$ , where $c$ is the total cost and $n$ is the number produced. What is $\mathrm{c}$ when no clocks are produced?

(Multiple Choice)

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Question 61

Find the length of the third side of the right triangle. Assume that $c$ represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places. - $\mathrm{a}=7, \mathrm{~b}=24$

(Multiple Choice)

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Question 62

Solve the equation. - $\sqrt{3 \mathrm{x}-2}+\sqrt{11+\mathrm{x}}=-1$

(Multiple Choice)

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Question 63

Find the length of the third side of the right triangle. Assume that $c$ represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places. - $b=8, c=16$

(Multiple Choice)

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Question 64

Rationalize the denominator and simplify. - $\frac{7-\sqrt{2}}{7+\sqrt{2}}$

(Multiple Choice)

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Question 65

Add or subtract. Simplify by collecting like radical terms, if possible. - $\sqrt{12 \mathrm{x}-12}+\sqrt{3 \mathrm{x}-3}$

(Multiple Choice)

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Question 66

Identify the radicand. - $6 x^{2} y^{2} \sqrt{\frac{2}{5 x-y}}$

(Multiple Choice)

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Question 67

Simplify. - $\sqrt{\frac{14}{\mathrm{r}^{4}}}$

(Multiple Choice)

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Question 68

Identify the radicand. - $\sqrt{\mathrm{y}-7}$

(Multiple Choice)

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Question 69

Simplify by factoring. - $\sqrt{9 m^{15} n^{4}}$

(Multiple Choice)

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Question 70

Simplify. - $\sqrt{49}$

(Multiple Choice)

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Question 71

Find the length of the third side of the right triangle. Assume that $c$ represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places. - $\mathrm{a}=6, \mathrm{~b}=8$

(Multiple Choice)

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Question 72

Perform the indicated operation. - $(\sqrt{3}-4)(\sqrt{2}+7)$

(Multiple Choice)

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Question 73

Add or subtract. Simplify by collecting like radical terms, if possible. - $7 \sqrt{18}-6 \sqrt{98}$

(Multiple Choice)

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Question 74

Multiply and then, if possible, simplify by factoring. - $\sqrt{\mathrm{x}-3} \sqrt{\mathrm{x}-3}$

(Multiple Choice)

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Question 75

Decide whether or not the radical expression represents a real number. - $-\sqrt{100}$

(True/False)

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Question 76

Perform the indicated operation. - $(2 \sqrt{7}+3 \sqrt{5})(10 \sqrt{7}+6 \sqrt{5})$

(Multiple Choice)

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Question 77

Rationalize the denominator and simplify. - $\frac{6}{\sqrt{\mathrm{k}}-5}$

(Multiple Choice)

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Question 78

Find the length of the third side of the right triangle. Assume that $c$ represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places. - $b=12, c=15$

(Multiple Choice)

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Question 79

Find the length of the third side of the right triangle. Where appropriate, give both an exact answer and an approximation to three decimal places. -

(Multiple Choice)

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Question 80

Solve the problem. -The cost of manufacturing clocks is given by $c=81 \sqrt{n+49}$ , where $c$ is the total cost and $n$ is the number produced. What is $\mathrm{c}$ when no clocks are produced?

Find the length of the third side of the right triangle. Assume that $c$ represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places. - $\mathrm{a}=7, \mathrm{~b}=24$

Solve the equation. - $\sqrt{3 \mathrm{x}-2}+\sqrt{11+\mathrm{x}}=-1$

Find the length of the third side of the right triangle. Assume that $c$ represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places. - $b=8, c=16$

Rationalize the denominator and simplify. - $\frac{7-\sqrt{2}}{7+\sqrt{2}}$

Add or subtract. Simplify by collecting like radical terms, if possible. - $\sqrt{12 \mathrm{x}-12}+\sqrt{3 \mathrm{x}-3}$

Identify the radicand. - $6 x^{2} y^{2} \sqrt{\frac{2}{5 x-y}}$

Simplify. - $\sqrt{\frac{14}{\mathrm{r}^{4}}}$

Identify the radicand. - $\sqrt{\mathrm{y}-7}$

Simplify by factoring. - $\sqrt{9 m^{15} n^{4}}$

Simplify. - $\sqrt{49}$

Find the length of the third side of the right triangle. Assume that $c$ represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places. - $\mathrm{a}=6, \mathrm{~b}=8$

Perform the indicated operation. - $(\sqrt{3}-4)(\sqrt{2}+7)$

Add or subtract. Simplify by collecting like radical terms, if possible. - $7 \sqrt{18}-6 \sqrt{98}$

Multiply and then, if possible, simplify by factoring. - $\sqrt{\mathrm{x}-3} \sqrt{\mathrm{x}-3}$

Decide whether or not the radical expression represents a real number. - $-\sqrt{100}$

Perform the indicated operation. - $(2 \sqrt{7}+3 \sqrt{5})(10 \sqrt{7}+6 \sqrt{5})$

Rationalize the denominator and simplify. - $\frac{6}{\sqrt{\mathrm{k}}-5}$

Find the length of the third side of the right triangle. Assume that $c$ represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places. - $b=12, c=15$

Find the length of the third side of the right triangle. Where appropriate, give both an exact answer and an approximation to three decimal places. -

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Rational Expressions and Equations

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Exam 8: Radical Expressions and Equations

Solve the problem. -The cost of manufacturing clocks is given by c=81n+49c=81 \sqrt{n+49}c=81n+49​ , where ccc is the total cost and nnn is the number produced. What is c\mathrm{c}c when no clocks are produced?

Find the length of the third side of the right triangle. Assume that ccc represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places. - a=7, b=24\mathrm{a}=7, \mathrm{~b}=24a=7, b=24

Solve the equation. - 3x−2+11+x=−1\sqrt{3 \mathrm{x}-2}+\sqrt{11+\mathrm{x}}=-13x−2​+11+x​=−1

Find the length of the third side of the right triangle. Assume that ccc represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places. - b=8,c=16b=8, c=16b=8,c=16

Rationalize the denominator and simplify. - 7−27+2\frac{7-\sqrt{2}}{7+\sqrt{2}}7+2​7−2​​

Add or subtract. Simplify by collecting like radical terms, if possible. - 12x−12+3x−3\sqrt{12 \mathrm{x}-12}+\sqrt{3 \mathrm{x}-3}12x−12​+3x−3​

Identify the radicand. - 6x2y225x−y6 x^{2} y^{2} \sqrt{\frac{2}{5 x-y}}6x2y25x−y2​​

Simplify. - 14r4\sqrt{\frac{14}{\mathrm{r}^{4}}}r414​​

Identify the radicand. - y−7\sqrt{\mathrm{y}-7}y−7​

Simplify by factoring. - 9m15n4\sqrt{9 m^{15} n^{4}}9m15n4​

Simplify. - 49\sqrt{49}49​

Find the length of the third side of the right triangle. Assume that ccc represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places. - a=6, b=8\mathrm{a}=6, \mathrm{~b}=8a=6, b=8

Perform the indicated operation. - (3−4)(2+7)(\sqrt{3}-4)(\sqrt{2}+7)(3​−4)(2​+7)

Add or subtract. Simplify by collecting like radical terms, if possible. - 718−6987 \sqrt{18}-6 \sqrt{98}718​−698​

Multiply and then, if possible, simplify by factoring. - x−3x−3\sqrt{\mathrm{x}-3} \sqrt{\mathrm{x}-3}x−3​x−3​

Decide whether or not the radical expression represents a real number. - −100-\sqrt{100}−100​

Perform the indicated operation. - (27+35)(107+65)(2 \sqrt{7}+3 \sqrt{5})(10 \sqrt{7}+6 \sqrt{5})(27​+35​)(107​+65​)

Rationalize the denominator and simplify. - 6k−5\frac{6}{\sqrt{\mathrm{k}}-5}k​−56​

Find the length of the third side of the right triangle. Assume that ccc represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places. - b=12,c=15b=12, c=15b=12,c=15

Find the length of the third side of the right triangle. Where appropriate, give both an exact answer and an approximation to three decimal places. -

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Rational Expressions and Equations

Systems of Equations

Quadratic Equations

Equations of Lines and Simplifying Radical Expressions

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Solve the problem. -The cost of manufacturing clocks is given by $c=81 \sqrt{n+49}$ , where $c$ is the total cost and $n$ is the number produced. What is $\mathrm{c}$ when no clocks are produced?

Find the length of the third side of the right triangle. Assume that $c$ represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places. - $\mathrm{a}=7, \mathrm{~b}=24$

Solve the equation. - $\sqrt{3 \mathrm{x}-2}+\sqrt{11+\mathrm{x}}=-1$

Find the length of the third side of the right triangle. Assume that $c$ represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places. - $b=8, c=16$

Rationalize the denominator and simplify. - $\frac{7-\sqrt{2}}{7+\sqrt{2}}$

Add or subtract. Simplify by collecting like radical terms, if possible. - $\sqrt{12 \mathrm{x}-12}+\sqrt{3 \mathrm{x}-3}$

Identify the radicand. - $6 x^{2} y^{2} \sqrt{\frac{2}{5 x-y}}$

Simplify. - $\sqrt{\frac{14}{\mathrm{r}^{4}}}$

Identify the radicand. - $\sqrt{\mathrm{y}-7}$

Simplify by factoring. - $\sqrt{9 m^{15} n^{4}}$

Simplify. - $\sqrt{49}$

Find the length of the third side of the right triangle. Assume that $c$ represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places. - $\mathrm{a}=6, \mathrm{~b}=8$

Perform the indicated operation. - $(\sqrt{3}-4)(\sqrt{2}+7)$

Add or subtract. Simplify by collecting like radical terms, if possible. - $7 \sqrt{18}-6 \sqrt{98}$

Multiply and then, if possible, simplify by factoring. - $\sqrt{\mathrm{x}-3} \sqrt{\mathrm{x}-3}$

Decide whether or not the radical expression represents a real number. - $-\sqrt{100}$

Perform the indicated operation. - $(2 \sqrt{7}+3 \sqrt{5})(10 \sqrt{7}+6 \sqrt{5})$

Rationalize the denominator and simplify. - $\frac{6}{\sqrt{\mathrm{k}}-5}$

Find the length of the third side of the right triangle. Assume that $c$ represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places. - $b=12, c=15$