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Algebra II : Radicals

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Example Questions

Example Question #21 : Solving And Graphing Radicals

Solve the equation: $\sqrt{2x}-3 = x$

Possible Answers:

$-2 i\sqrt{5}$

$-5\pm i\sqrt{2}$

$4+\sqrt{7}$

$-2\pm i\sqrt{5}$

Correct answer:

$-2\pm i\sqrt{5}$

Explanation:

Add three on both sides.

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

$\sqrt{2x}=x+3$

Square both sides.

2x=(x+3)^2

Use the FOIL method to expand the right side.

2x=(x)(x)+(x)(3)+3(x)+3(3)

2x=x^2+6x+9

Subtract from both sides. The equation becomes:

0=x^2+4x+9

Use the quadratic equation to determine the roots.

$x=\frac{-4\pm \sqrt{(4^2)-4(1)(9)}}{2(1)}= \frac{-4\pm \sqrt{16-36}}{2}$

Simplify the radical.

$= \frac{-4\pm \sqrt{-20}}{2} = \frac{-4\pm( \sqrt{-1}\times \sqrt{2}\times \sqrt{2} \times \sqrt{5})}{2}$

$=\frac{-4\pm 2i\sqrt5}{2}$

Reduce the fraction.

$=-2\pm i\sqrt{5}$

The answers are: $-2\pm i\sqrt{5}$

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Example Question #1572 : Mathematical Relationships And Basic Graphs

Solve: $\sqrt{3x}-5 =8$

Possible Answers:

$\frac{1}{27}$

$\frac{169}{3}$

$\frac{1}{9}$

Correct answer:

$\frac{169}{3}$

Explanation:

Add five on both sides.

$\sqrt{3x}-5 +5=8+5$

Simplify both sides of the equation.

$\sqrt{3x}=13$

Square both sides.

$(\sqrt{3x})^2=(13)^2$

3x=169

Divide both sides by three.

$\frac{3x}{3}=\frac{169}{3}$

$x=\frac{169}{3}$

The answer is: $\frac{169}{3}$

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Example Question #21 : Solving Radical Equations

Solve: $\sqrt{3x+2}+3= 10$

Possible Answers:

$\frac{194}{3}$

$\frac{9}{4}$

$\frac{194}{7}$

$\frac{37}{3}$

$\frac{47}{3}$

Correct answer:

$\frac{47}{3}$

Explanation:

To isolate the x-variable, first subtract three from both sides.

$\sqrt{3x+2}+3-3= 10-3$

$\sqrt{3x+2}=7$

Square both sides.

$(\sqrt{3x+2})^2=7^2$

The equation becomes:

3x+2=49

Subtract two from both sides.

3x+2-2=49-2

3x=47

Divide by three on both sides.

$x=\frac{47}{3}$

The answer is: $\frac{47}{3}$

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Example Question #21 : Solving Radical Equations

Solve: $\sqrt{3x-4}-8 = -10$

Possible Answers:

$\frac{22}{3}$

$\pm \frac{8}{3}$

$\textup{No solution.}$

$\frac{3}{8}$

$\frac{8}{3}$

Correct answer:

$\textup{No solution.}$

Explanation:

Add eight on both sides.

$\sqrt{3x-4}-8 +(8)= -10+(8)$

$\sqrt{3x-4}=-2$

Notice that the range of the parent function $y=\sqrt{x}$ must be greater than zero. There will be no values of square root that will equal to negative two.

The answer is: $\textup{No solution.}$

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Example Question #22 : Solving Radical Equations

Solve the equation: $\sqrt{x+2} =\sqrt{ 2(x-1)}$

Possible Answers:

$\textup{There is no solution.}$

$2\sqrt2$

$\sqrt2$

Correct answer:

Explanation:

In order to eliminate the radicals, simply square both sides.

$(\sqrt{x+2} )^2=(\sqrt{ 2(x-1)})^2$

The equation becomes:

x+2= 2(x-1)

Simplify the right side by distribution.

x+2= 2x-2

Subtract from both sides. The equation becomes:

2= x-2

Add 2 on both sides and simplify both sides.

2+2= x-2+2

The answer is: x=4

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Example Question #4246 : Algebra Ii

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

Possible Answers:

$\frac{7}{2}$

$\frac{7}{3}$

$\textup{There is no solution.}$

$\frac{3}{2}$

Correct answer:

$\frac{7}{2}$

Explanation:

Divide by two on both sides.

$\frac{2\sqrt{2x-3}}{2} = \frac{4}{2}$

The equation becomes: $\sqrt{2x-3} = 2$

Square both sides.

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

2x-3=4

Add three on both sides.

2x=7

Divide by two on both sides.

$\frac{2x}{2}=\frac{7}{2}$

The answer is: $\frac{7}{2}$

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Example Question #1581 : Mathematical Relationships And Basic Graphs

Solve the equation: $\sqrt{6-x}+2 = 16$

Possible Answers:

400

$\textup{There is no solution.}$

Correct answer:

Explanation:

Subtract two from both sides.

$\sqrt{6-x}+2 -(2)= 16-(2)$

Simplify the equation.

$\sqrt{6-x} = 14$

Square both sides.

$(\sqrt{6-x})^2 =( 14)^2$

6-x=196

Add on both sides.

6-x+x=196+x

6=196+x

Subtract 196 on both sides.

6-196=196+x-196

The answer is:

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Example Question #31 : Solving Radical Equations

Solve: $\sqrt{9x+2}-4=10$

Possible Answers:

$\textup{There is no solution.}$

$\frac{26}{9}$

$\frac{172}{9}$

$\frac{98}{9}$

$\frac{194}{9}$

Correct answer:

$\frac{194}{9}$

Explanation:

Add four on both sides to isolate the radical.

$\sqrt{9x+2}-4+4=10+4$

Simplify both sides.

$\sqrt{9x+2}= 14$

Square both sides.

$(\sqrt{9x+2})^2= (14)^2$

9x+2=196

Subtract two from both sides.

9x=194

Divide by nine on both sides.

$\frac{9x}{9}=\frac{194}{9}$

The answer is: $\frac{194}{9}$

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Example Question #4249 : Algebra Ii

Solve the equation: $\sqrt{2x-3}-19=6$

Possible Answers:

376

314

$\textup{The answer is not given.}$

Correct answer:

314

Explanation:

Add 19 on both sides.

$\sqrt{2x-3}-19+(19)=6+(19)$

Simplify both sides.

$\sqrt{2x-3} = 25$

Square both sides.

$(\sqrt{2x-3})^2= 25^{2}$

2x-3=625

Add three on both sides.

2x-3+3=625+3

2x=628

Divide by two on both sides.

$\frac{2x}{2}=\frac{628}{2}$

Reduce the fractions.

The answer is: 314

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Example Question #31 : Solving And Graphing Radicals

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

Possible Answers:

$-\frac{1}{6}$

$\textup{No solution.}$

Correct answer:

Explanation:

Square both sides of the equation.

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

Simplify both sides.

-3x-9 = 9

Add nine on both sides.

-3x-9 +9= 9+9

-3x=18

Divide both sides by negative three.

$\frac{-3x}{-3}=\frac{18}{-3}$

Simplify both fractions.

x=-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 #21 : Solving And Graphing Radicals

Example Question #1572 : Mathematical Relationships And Basic Graphs

Example Question #21 : Solving Radical Equations

Example Question #21 : Solving Radical Equations

Example Question #22 : Solving Radical Equations

Example Question #4246 : Algebra Ii

Example Question #1581 : Mathematical Relationships And Basic Graphs

Example Question #31 : Solving Radical Equations

Example Question #4249 : Algebra Ii

Example Question #31 : Solving And Graphing Radicals

All Algebra II Resources

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