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Algebra II : Solving Radical Equations

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Example Question #41 : Solving And Graphing Radicals

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

Possible Answers:

$\textup{There is no solution.}$

$\frac{13}{5}$

$\frac{26}{5}$

$\frac{293}{5}$

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 #42 : Solving And Graphing Radicals

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

Possible Answers:

$\frac{43}{36}$

$-\frac{17}{108}$

$\frac{41}{96}$

$\frac{145}{108}$

$\frac{919}{108}$

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: $\frac{3367}{6}$

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Example Question #44 : Solving And Graphing 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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Example Question #45 : Solving And Graphing Radicals

Solve the equation: $\sqrt[5]{2x-6} = 2$

Possible Answers:

$\textup{There is no solution.}$

Correct answer:

Explanation:

Raise both sides of the equation by five.

$(\sqrt[5]{2x-6} )^5= 2^5$

2x-6 = 32

Add six on both sides.

2x-6 +6= 32+6

2x=38

Divide by two on both sides.

$\frac{2x}{2}=\frac{38}{2}$

Simplify both sides.

The answer is:

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Example Question #46 : Solving And Graphing Radicals

Solve: $\sqrt{\frac{3}{2}x-1} = 5$

Possible Answers:

$36\sqrt{2}$

$24\sqrt{2}$

$\frac{26}{3}$

$\frac{52}{3}$

Correct answer:

$\frac{52}{3}$

Explanation:

Square both sides to eliminate the radical.

$(\sqrt{\frac{3}{2}x-1} )^2= 5^2$

The equation becomes:

$\frac{3}{2}x-1 = 25$

Add one on both sides.

$\frac{3}{2}x-1 +1= 25+1$

$\frac{3}{2}x = 26$

Multiply two-thirds on both sides to isolate the x-variable.

$\frac{3}{2}x \cdot \frac{2}{3}= 26\cdot \frac{2}{3}$

Simplify both sides.

The answer is: $\frac{52}{3}$

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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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Algebra II : Solving Radical Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #41 : Solving And Graphing Radicals

Example Question #42 : Solving And Graphing Radicals

Example Question #43 : Solving And Graphing Radicals

Example Question #44 : Solving And Graphing Radicals

Example Question #45 : Solving And Graphing Radicals

Example Question #46 : Solving And Graphing Radicals

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

All Algebra II Resources

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