Equations with Square and Cube Roots

Solving Equations with Square Roots

By the end of the lesson, you will be able to solve an equation using square roots and cube roots

Multiple Choice

Square root is the inverse of ____________.

• Cube Roots

• Squaring

• Multiplication

• Absolute Value

These equations have more than one answer!

Multiple Choice

How do you solve the equation: $$x^2\ =\ 100$$  

• Take  $$100^2$$  

• Take  $$\sqrt{100}$$  

• Multiply 100 by 2 

Multiple Choice

How many solutions do Squared Equations have?  Example: $$m^2=16$$  

• 1

• 2

• 3

Multiple Choice

Is the equation solved correctly?

$$x^2=25$$  

$$\sqrt{x^2}=\sqrt{25}$$  

$$x=5$$  

• YES

• NO

Multiple Choice

Is the equation solved correctly?

$$x^2=64$$  

$$\sqrt{x^2}=\sqrt{64}$$  

$$x=\pm8$$  

• YES

• NO

Multiple Choice

Is the equation solved correctly?

  $$x^2=81$$  

$$\sqrt{x^2}=\sqrt{81}$$  

$$x=\pm9$$  

• YES

• NO

Multiple Select

Solve

$$y^2=100$$  

• y=-10

• y=-9

• y=10

• y=9

• y=3

Multiple Select

Solve

$$x^2=169$$  

• x=12

• x=13

• x=-12

• x=-11

• x=-13

Multiple Select

Solve for x: $$x^2=\ 49$$  

• x = -7

• x = -9 

• x = 7

• x = 9

Multiple Select

Solve

$$y^2=36$$  

• y=-6

• y=-9

• y=6

• y=9

• y=3

Multiple Choice

Cube roots are the opposite of ____________.

• Cube a number

• Squaring

• Multiplication

• Absolute Value

Multiple Choice

How many solutions do Cubed Equations have?  Example: $$m^3=-27$$  

• 1

• 2

• 3

Multiple Choice

How do you solve the equation: $$x^3\ =\ 343$$  

• Take  $$343^3$$  

• Take  $$\sqrt[3]{343}$$  

• Multiply 343 by 2 

Multiple Choice

Is the equation solved correctly?

  $$x^3=-64$$  

$$\sqrt[3]{x^3}=\sqrt[3]{-64}$$  

$$x=-4$$  

• YES

• NO

Multiple Choice

Is the equation solved correctly?

$$x^3=125$$  

$$\sqrt[3]{x^3}=\sqrt[3]{125}$$   

$$x=-5$$   

• YES

• NO

Multiple Choice

• x = -5

• x = 5

• x = 10

• x = 12

Multiple Choice

• x = 11

• x = 6

• x = -6

• x = 12

Multiple Choice

• x = 12

• x = 8

• x = -8

• x= 11

Multiple Choice

• x = -9

• x = 10

• x = 11

• x = 9

Multiple Choice

• $$x\ =\ \frac{1}{3}$$

• x = 3

• $$x\ =\ \frac{1}{9}$$

Multiple Choice

• $$x\ =\ -\frac{5}{12}$$

• $$x\ =\ -\frac{7}{9}$$

• $$x\ =\ -\frac{2}{25}$$

Multiple Choice

$$x^2=\frac{4}{81}$$  

• $$\pm\frac{2}{8}$$  

• $$\pm\frac{2}{9}$$  

• $$\pm\frac{1}{9}$$  

• $$\pm\frac{1}{8}$$  

Multiple Choice

$$x^2=\frac{1}{144}$$  

• $$\pm\frac{1}{12}$$  

• $$\pm\frac{1}{11}$$  

• $$\pm\frac{1}{10}$$  

Poll

How well did you understand this lesson?