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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #47 : Solving And Graphing Radicals

Solve: $\frac{2}{\sqrt{2x}}+4=8$

Possible Answers:

$\frac{1}{4}$

$\textup{No solution.}$

$\frac{1}{16}$

$\frac{1}{8}$

$\frac{1}{64}$

Correct answer:

$\frac{1}{8}$

Explanation:

Subtract both sides by four.

$\frac{2}{\sqrt{2x}}+4-4=8-4$

$\frac{2}{\sqrt{2x}}=4$

Multiply by the denominator on both sides. The equation becomes:

$2=4\sqrt{2x}$

Divide by four on both sides to isolate the radical.

$\frac{2}{4}=\frac{4\sqrt{2x}}{4}$

$\frac{1}{2} = \sqrt{2x}$

Square both sides.

$\frac{1}{4} = 2x$

Divide by two on both sides.

The answer is: $\frac{1}{8}$

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Example Question #48 : Solving And Graphing Radicals

Solve the radical equation: $\sqrt[5]{9x-3}+3 = 5$

Possible Answers:

$\frac{13}{9}$

$\frac{35}{9}$

$\frac{32765}{9}$

$-\frac{35}{9}$

$\frac{32771}{9}$

Correct answer:

$\frac{35}{9}$

Explanation:

Subtract three on both sides.

$\sqrt[5]{9x-3}+3 -3= 5-3$

$\sqrt[5]{9x-3} = 2$

Take the fifth power of both sides to cancel the radical.

$(\sqrt[5]{9x-3})^5 = 2^5$

9x-3 = 32

Add three on both sides.

9x-3 +3= 32+3

9x=35

Divide by nine on both sides.

$\frac{9x}{9}=\frac{35}{9}$

The answer is: $\frac{35}{9}$

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Example Question #49 : Solving And Graphing Radicals

Solve the radical equation: $\sqrt{3x-9} = 27$

Possible Answers:

240

$\textup{No solution.}$

246

$20\sqrt3$

Correct answer:

246

Explanation:

Square both sides to eliminate the radical.

$(\sqrt{3x-9} )^2= 27^{2}$

3x-9 = 729

Add 9 on both sides.

3x=738

Divide by three on both sides.

$\frac{3x}{3}=\frac{738}{3}$

The answer is: 246

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Example Question #50 : Solving And Graphing Radicals

Solve the equation: $\sqrt{9x-2}-7 =1$

Possible Answers:

$\frac{11}{3}$

$\frac{22}{3}$

$\frac{33}{2}$

Correct answer:

$\frac{22}{3}$

Explanation:

Add 7 on both sides.

$\sqrt{9x-2}-7+7 =1+7$

$\sqrt{9x-2} =8$

Square both sides.

$(\sqrt{9x-2}) ^2=8^2$

Simplify both sides of the equation.

9x-2 =64

Add 2 on both sides.

9x-2+2 =64+2

9x=66

Divide by nine on both sides.

$\frac{9x}{9}=\frac{66}{9}$

Reduce both fractions.

$x=\frac{66}{9}=\frac{3\times 11\times 2}{3\times 3} =\frac{22}{3}$

The answer is: $\frac{22}{3}$

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Example Question #51 : Solving And Graphing Radicals

Solve the equation: $\sqrt[3]{7x-1}+5 = 8$

Possible Answers:

$\frac{26}{7}$

$\frac{2196}{7}$

$\frac{1}{4}$

Correct answer:

Explanation:

In order to solve this equation, first add five on both sides.

$\sqrt[3]{7x-1}+5 -5= 8-5$

The equation becomes: $\sqrt[3]{7x-1}=3$

Cube both sides.

$(\sqrt[3]{7x-1})^3=3^3$

Simplify both sides of the equation.

7x-1 = 27

Add one on both sides.

7x-1 +1= 27+1

7x=28

Divide both sides by seven.

$\frac{7x}{7}=\frac{28}{7}$

The answer is:

Report an Error

Example Question #361 : Radicals

Solve the equation: $\sqrt[4]{2x+6}+6 = 8$

Possible Answers:

Correct answer:

Explanation:

Subtract six from both sides.

$\sqrt[4]{2x+6}+6 -6= 8-6$

Simplify the equation.

$\sqrt[4]{2x+6} =2$

Take the fourth power of both sides.

$(\sqrt[4]{2x+6}) ^4=2^4$

2x+6=16

Subtract six from both sides.

2x+6-6=16-6

2x=10

Divide by two on both sides.

$\frac{2x}{2}=\frac{10}{2}$

Reduce the fractions.

The answer is:

Report an Error

Example Question #53 : Solving And Graphing Radicals

Solve the equation: $\sqrt{2x}+2= \sqrt8$

Possible Answers:

$4-\sqrt2$

$3+8\sqrt2$

$8-4\sqrt2$

$6-4\sqrt2$

$4-3\sqrt2$

Correct answer:

$6-4\sqrt2$

Explanation:

Subtract two from both sides.

$\sqrt{2x}+2-2= \sqrt8-2$

$\sqrt{2x}= \sqrt8-2$

Square both sides. Use the FOIL method to simplify the right side.

$(\sqrt{2x})^2= (\sqrt8-2)^2$

$2x=(\sqrt8)(\sqrt8)+(\sqrt8)(-2)+(-2)(\sqrt8)+(-2)(-2)$

$2x= 8-4\sqrt8+4$

Combine like terms.

$2x= 12-4\sqrt8$

The term $\sqrt8$ can be rewritten as: $2\sqrt2$

$2x= 12-4\cdot 2\sqrt2$

$2x= 12-8\sqrt2$

Divide by two on both sides.

$\frac{2x}{2}= \frac{12-8\sqrt2}{2}$

The answer is: $6-4\sqrt2$

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Example Question #361 : Radicals

Solve the radical equation: $\sqrt{4x-8}-3 = 6$

Possible Answers:

$\frac{1}{4}$

$\frac{17}{4}$

$\frac{89}{4}$

$\frac{89}{2}$

$\frac{23}{8}$

Correct answer:

$\frac{89}{4}$

Explanation:

Add three on both sides.

$\sqrt{4x-8}-3 +3= 6+3$

$\sqrt{4x-8} = 9$

Square both sides of the equation.

$(\sqrt{4x-8})^2 = 9^2$

4x-8 = 81

Add 8 on both sides.

4x=89

Divide by four on both sides.

$\frac{4x}{4}=\frac{89}{4}$

The answer is: $\frac{89}{4}$

Report an Error

Example Question #4271 : Algebra Ii

Solve the radical equation: $\sqrt[4]{2x+16}+5=8$

Possible Answers:

$\frac{65}{4}$

$\frac{128}{3}$

$\frac{256}{9}$

$\frac{65}{2}$

$\frac{256}{3}$

Correct answer:

$\frac{65}{2}$

Explanation:

Subtract five from both sides.

$\sqrt[4]{2x+16}+5-5=8-5$

The equation becomes:

$\sqrt[4]{2x+16}=3$

Raise both sides by the power of four to eliminate the radical.

$(\sqrt[4]{2x+16})^4=3^4$

2x+16=81

Subtract 16 on both sides.

2x+16-16=81-16

2x=65

Divide by two on both sides.

$\frac{2x}{2}=\frac{65}{2}$

The answer is: $\frac{65}{2}$

Report an Error

Example Question #4272 : Algebra Ii

Solve the equation: $\sqrt{8x-3} = 30$

Possible Answers:

$\frac{57}{8}$

$\frac{903}{8}$

$\frac{63}{8}$

$\frac{897}{8}$

$\frac{903}{4}$

Correct answer:

$\frac{903}{8}$

Explanation:

$(\sqrt{8x-3}) ^2= 30^2$

8x-3 = 900

Add three on both sides.

8x-3 +3= 900+3

8x=903

Divide by 8 on both sides.

$\frac{8x}{8}=\frac{903}{8}$

The answer is: $\frac{903}{8}$

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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #47 : Solving And Graphing Radicals

Example Question #48 : Solving And Graphing Radicals

Example Question #49 : Solving And Graphing Radicals

Example Question #50 : Solving And Graphing Radicals

Example Question #51 : Solving And Graphing Radicals

Example Question #361 : Radicals

Example Question #53 : Solving And Graphing Radicals

Example Question #361 : Radicals

Example Question #4271 : Algebra Ii

Example Question #4272 : Algebra Ii

All Algebra II Resources

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