Square and Cube Root Equations

LEQ: How do we simplify cube roots?

​Standard: 8.EE.2

Use square root and cube root symbols to represent solutions to equations. Recognize that x2 = p (where p is a positive rational number and lxl < 25) has 2 solutions and x3 = p (where p is a negative or positive rational number and lxl < 10) has one solution. Evaluate square roots of perfect squares < 625 and cube roots of perfect cubes > -1000 and < 1000.

8th Grade| Math

8.EE.2​

Learning Targets for 8.EE.2

​ K1: I can evaluate square roots and cube roots of perfect squares < 625

 K2: I can evaluate cube roots of perfect cubes >-1000 and <1000.

 K3: I can solve equations with exponents with powers of 2 using square or cube roots.

8th Grade | Math

MGSE8.EE.2​

Definitions:

Cube Root: The cube root of a number is the answer to what number times itself three times equals the original number. For example, the cube root of 27 would be 3 because 3 X 3  X 3 = 27.

Perfect Cube: A perfect cube is any number that can be obtained by multiplying a number by itself 3 times. For example, 64 is a perfect cube because 64 = 4 X 4  X 4.

Subject | Subject

Some text here about the topic of discussion

Fill in the Blanks

Evaluate

$\sqrt{25}$  

Fill in the Blanks

Evaluate

$\sqrt{81}$  

Fill in the Blanks

Emily wants to buy a tablecloth to cover a square card table. She knows the tabletop has an area of 9 square feet. What are the minimum dimensions of the tablecloth Emily needs.

Emily should buy a tablecloth that measures at least ____ feet by ____ feet.

Multiple Choice

$$^{3\sqrt{8}}$$  

• $$\frac{8}{3}$$  

• $$2$$  

• $$512$$  

• $$5$$  

Fill in the Blanks

Evaluate cube root of 1

Fill in the Blanks

Evaluate cube root of 27.

Fill in the Blanks

A cube-shaped art sculpture has a volume of 64 cubic feet. What is the length of each edge of the cube?

The length of each edge is

feet.

Negative Cubed Roots

Remember, a cubed root can be negative. To find the cubed root of -27, you need to find your perfect cube. 27 is 3 x 3 x 3. When you multiply - 3 x -3 x -3, you will get -27. The answer for this problem is -3.

Fill in the Blanks

$\sqrt[3]{-343}=$  

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

• $$x\ =\ \frac{3}{12}$$

• $$x\ =\ \frac{16}{12}$$

• $$x\ =\ \frac{1}{2}$$

• $$x\ =\ \frac{4}{5}$$

Multiple Choice

• $$x\ =\ \frac{1}{3}$$

• $$x\ =\ \frac{3}{9}$$

• $$x\ =\ -\frac{1}{3}$$

Multiple Choice

What is the inverse operations of x³?

• cubed root

• square root

• multiplication

• division

Multiple Choice

Would you classify 45 as a perfect square a perfect cube or neither?

• Perfect Square

• Perfect Cube

• Neither

Multiple Choice

Would you classify 36 as a perfect square, a perfect cube or neither?

• Perfect Square

• Perfect Cube

• Neither