The square of a number is that number . The square of an integer is a . The square of negative 12 is written as . The opposite of the square of 12 is written as .
2 • 2 = 4. Another number that can be multiplied by itself to equal 4 is .
2. Fill in the blanks with square root or principal square root.
A is a number that produces a given number when it is multiplied by itself.
The is the positive square root of a number and is shown using the radical symbol, √.
3. Complete the table to describe perfect cubes.
DefinitionA number multiplied by itself times.
Examples13 = 1 • 1 • 1 =
23 = • • = 8
3 = 4 • 4 • 4 =
4. Answer the questions about cube roots.
What is a cube root?

Use the radical symbol to represent the cube root of 8.

What is the cube root of –8?

Main idea: Solving equations by taking the square root
5. Complete the steps to show how to solve x2 = 36.

6. Answer the questions about Ally's web page icons as you work through the problem in the study.
Each icon contains 1024 pixels arranged in rows. What does p represent in the equation p2 = 1024?

What is the first step in solving p2 = 1024?

Why doesn't the solution p = –32 make sense for this problem?

Main idea: Solving equations by taking the cube root
7. Solving an equation in the form x3 = p is similar to solving equations with squared terms. Complete the table to show the differences.

x2 = px3 = p
To solve:Take the square root.

Number of solutions and their sign(s):Two solutions. One is positive and one is negative.

Example:

8. Answer the questions about Tanisha's baking supply container as you work through the problem in the study.
The volume of the salt container is 125 cm3. What does x represent in the equation x3 = 125?

What is the first step in solving x3 = 125?

Is x = –5 a solution to the equation? Why or why not?

Key Terms
Use this table to write definitions for the key terms from this activity in your own words. If you're confident you know a term, put a check mark next to it and move on.

Key TermDefinition
cube

cube root

integer

inverse operations

perfect square

principal square root

square

square root

I