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Algebra II : Radicals

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Example Questions

Example Question #1581 : Mathematical Relationships And Basic Graphs

Solve the equation: $\sqrt{3-3x}+6 =10$

Possible Answers:

$-\frac{7}{3}$

$-\frac{13}{3}$

$-\frac{7}{3}$

$-\frac{19}{3}$

$\textup{No solution.}$

Correct answer:

$-\frac{13}{3}$

Explanation:

Subtract six from both sides.

$\sqrt{3-3x}+6-6 =10-6$

$\sqrt{3-3x}=4$

Square both sides.

$(\sqrt{3-3x})^2=4^2$

3-3x=16

Add on both sides.

3-3x+3x=16+3x

3=16+3x

Subtract 16 from both sides.

3-16=16+3x-16

-13 = 3x

Divide by three on both sides.

$\frac{-13 }{3}=\frac{ 3x}{3}$

The answer is: $-\frac{13}{3}$

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Example Question #31 : Solving And Graphing Radicals

Solve the equation: $-\sqrt{-9x}-3 =- 8$

Possible Answers:

$-\frac{4}{3}$

$\textup{There is no solution.}$

$-\frac{31}{9}$

$-\frac{5}{9}$

$-\frac{25}{9}$

Correct answer:

$-\frac{25}{9}$

Explanation:

Add three on both sides.

$-\sqrt{-9x}-3 +3=- 8+3$

$-\sqrt{-9x} = -5$

Divide by negative one to isolate the radical.

$\frac{-\sqrt{-9x}}{-1} = \frac{-5}{-1}$

The equation becomes: $\sqrt{-9x} =5$

Square both sides.

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

-9x=25

Divide by negative nine on both sides.

$\frac{-9x}{-9}=\frac{25}{-9}$

The answer is: $-\frac{25}{9}$

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Example Question #33 : Solving Radical Equations

Solve the equation: $\sqrt{5x+3}+16= 25$

Possible Answers:

412

$\frac{1678}{5}$

$\frac{78}{5}$

$\frac{84}{5}$

Correct answer:

$\frac{78}{5}$

Explanation:

Solve by first subtracting 16 on both sides.

$\sqrt{5x+3}+16-16= 25-16$

The equation becomes:

$\sqrt{5x+3} =9$

Square both sides.

$(\sqrt{5x+3})^2 =9^2$

5x+3=81

Subtract three on both sides.

5x+3-3=81-3

5x=78

Divide by five on both sides.

$\frac{5x}{5}=\frac{78}{5}$

The answer is: $\frac{78}{5}$

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Example Question #1592 : Mathematical Relationships And Basic Graphs

Solve the equation: $\sqrt[3]{3x}+6=8$

Possible Answers:

$\frac{3}{2}$

$\frac{8}{3}$

Correct answer:

$\frac{8}{3}$

Explanation:

Subtract six from both sides.

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

Simplify both sides.

$\sqrt[3]{3x} = 2$

Cube both sides to eliminate the cube root.

3x= 2^3

3x=8

Divide by three on both sides.

$\frac{3x}{3}=\frac{8}{3}$

The answer is: $\frac{8}{3}$

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Example Question #352 : Radicals

Solve the equation: $\sqrt[4]{3(x+1)}+16=18$

Possible Answers:

$\frac{26}{3}$

$\frac{26}{5}$

$\textup{There is no solution.}$

$\frac{13}{3}$

Correct answer:

$\frac{13}{3}$

Explanation:

Simplify by first subtracting 16 on both sides.

$\sqrt[4]{3(x+1)}+16-16=18-16$

$\sqrt[4]{3(x+1)}=2$

Raise both sides by the fourth power.

$(\sqrt[4]{3(x+1)})^4=2^4$

3(x+1)=16

Expand the binomial.

3x+3=16

Subtract three from both sides.

3x+3-3=16-3

3x=13

Divide by three on both sides.

$\frac{3x}{3}=\frac{13}{3}$

The answer is: $\frac{13}{3}$

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Example Question #32 : Solving And Graphing Radicals

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

Possible Answers:

$\textup{There is no solution.}$

Correct answer:

Explanation:

To eliminate the radical, we will need to cube both sides of the equation.

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

The equation becomes:

9-x = 27

Add on both sides.

9-x+(x) = 27+(x)

9=27+x

Subtract 27 from both sides.

9-27=27+x-27

x=-18

This answer is valid after re-substituting back to the original equation.

The answer is:

Report an Error

Example Question #41 : Solving Radical Equations

Solve the equation: $\sqrt{5x-4} +7 = 10$

Possible Answers:

$\frac{293}{5}$

$\textup{There is no solution.}$

$\frac{13}{5}$

$\frac{26}{5}$

Correct answer:

$\frac{13}{5}$

Explanation:

Subtract seven on both sides.

$\sqrt{5x-4} +7 -7= 10-7$

$\sqrt{5x-4} =3$

Square both sides. This will eliminate the radical on the left side.

$(\sqrt{5x-4} )^2=3^2$

5x-4 = 9

Add four on both sides.

5x-4 +4= 9+4

5x=13

Divide by five on both sides.

$\frac{5x}{5}=\frac{13}{5}$

The answer is: $\frac{13}{5}$

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Example Question #4256 : Algebra Ii

Solve the equation: $3\sqrt[3]{4x-3} -3= 1$

Possible Answers:

$-\frac{17}{108}$

$\frac{43}{36}$

$\frac{919}{108}$

$\frac{41}{96}$

$\frac{145}{108}$

Correct answer:

$\frac{145}{108}$

Explanation:

Add three on both sides.

$3\sqrt[3]{4x-3} -3+3= 1+3$

$3\sqrt[3]{4x-3}=4$

Divide by three on both sides.

$\frac{3\sqrt[3]{4x-3}}{3}=\frac{4}{3}$

$\sqrt[3]{4x-3}=\frac{4}{3}$

Cube both sides to eliminate the radical. Simplify both sides.

$(\sqrt[3]{4x-3})^3=(\frac{4}{3})^3$

$4x-3 = \frac{64}{27}$

Add three on both sides. This is the same as adding $\frac{81}{27}$ on the right side.

$4x-3+3=\frac{64}{27}+\frac{81}{27}$

$4x= \frac{145}{27}$

Divide by four on both sides. This is similar to multiplying one fourth on both sides and will isolate the x-variable on the left.

$4x\cdot \frac{1}{4}= \frac{145}{27}\cdot \frac{1}{4}$

$x=\frac{145}{108}$

The answer is: $\frac{145}{108}$

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Example Question #43 : Solving And Graphing Radicals

Solve the equation: $\sqrt{6x-3}-28 = 30$

Possible Answers:

$\frac{1}{6}$

$\textup{There is no solution.}$

$\frac{3361}{6}$

$\frac{7}{6}$

$\frac{3367}{6}$

Correct answer:

$\frac{3367}{6}$

Explanation:

In order to solve this equation, first add 28 on both sides.

$\sqrt{6x-3}-28+28 = 30+28$

$\sqrt{6x-3}=58$

Square both sides.

$(\sqrt{6x-3})^2=58^2$

6x-3=3364

Add three on both sides.

6x-3+3=3364+3

6x=3367

Divide by six on both sides.

$\frac{6x}{6}=\frac{3367}{6}$

The answer is: $\frac{3367}{6}$

Report an Error

Example Question #351 : Radicals

Solve the equation: $\sqrt[3]{6x-2}= 4$

Possible Answers:

$\frac{31}{3}$

$\textup{There is no solution.}$

Correct answer:

Explanation:

Cube both sides.

$(\sqrt[3]{6x-2})^3= 4^3$

This will eliminate the radical.

6x-2= 64

Add two on both sides.

6x-2+2= 64+2

6x=66

Divide by six on both sides.

$\frac{6x}{6}=\frac{66}{6}$

The answer is:

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Algebra II : Radicals

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1581 : Mathematical Relationships And Basic Graphs

Example Question #31 : Solving And Graphing Radicals

Example Question #33 : Solving Radical Equations

Example Question #1592 : Mathematical Relationships And Basic Graphs

Example Question #352 : Radicals

Example Question #32 : Solving And Graphing Radicals

Example Question #41 : Solving Radical Equations

Example Question #4256 : Algebra Ii

Example Question #43 : Solving And Graphing Radicals

Example Question #351 : Radicals

All Algebra II Resources

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