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Questions and Answers
What is the cube root of $-27$?
What is the cube root of $-27$?
If the volume of a cube is $125 ext{ in}^{3}$, what is the edge length of the cube?
If the volume of a cube is $125 ext{ in}^{3}$, what is the edge length of the cube?
How would you evaluate the expression $( rac{ ext{cube root of } 125})^3 + 21$?
How would you evaluate the expression $( rac{ ext{cube root of } 125})^3 + 21$?
What is the simplified result of $2^3 - 216 - 3 - 2(-6)^3$?
What is the simplified result of $2^3 - 216 - 3 - 2(-6)^3$?
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Which expression is equivalent to finding the cube root of a number?
Which expression is equivalent to finding the cube root of a number?
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Study Notes
Cube Roots
- A cube root of a number is a number that, when multiplied by itself three times, equals the given number.
- A perfect cube is a number that can be written as the cube of an integer.
- The symbol ∛ represents a cube root.
Finding Cube Roots
- To find the cube root of a number, determine which integer, when cubed, results in the given number.
- Cubing a number and finding its cube root are inverse operations.
Evaluating Expressions Involving Cube Roots
- Evaluate the cube root first.
- Follow the order of operations (PEMDAS/BODMAS).
- Substitute given values for variables.
- Simplify the expression using multiplication and addition/subtraction.
Real-Life Application: Baseball Display Case
- Volume of a cube: V = s³ (where s is the edge length)
- Surface area of a cube: S = 6s²
- Example: A baseball display case with a volume of 125 cubic inches has an edge length of 5 inches. The surface area is 150 square inches.
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Description
Explore the concept of cube roots, including how to find them and evaluate expressions involving these mathematical principles. This quiz also highlights real-life applications, such as calculating the volume and surface area of a cube, with an example related to a baseball display case.
