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Questions and Answers
What is the cube root of $-27$?
What is the cube root of $-27$?
- -3 (correct)
- -2
- 3
- 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?
- 12 inches
- 10 inches
- 5 inches (correct)
- 15 inches
How would you evaluate the expression $( rac{ ext{cube root of } 125})^3 + 21$?
How would you evaluate the expression $( rac{ ext{cube root of } 125})^3 + 21$?
- 25 + 21 = 46
- 125 - 21 = 104
- 100 + 21 = 121
- 125 + 21 = 146 (correct)
What is the simplified result of $2^3 - 216 - 3 - 2(-6)^3$?
What is the simplified result of $2^3 - 216 - 3 - 2(-6)^3$?
Which expression is equivalent to finding the cube root of a number?
Which expression is equivalent to finding the cube root of a number?
Flashcards
Cube root
Cube root
A number that, when multiplied by itself three times, equals a given number. For example, the cube root of 8 is 2 because 2 x 2 x 2 = 8.
Perfect cube
Perfect cube
A number that results from cubing an integer. In other words, it's the product of an integer multiplied by itself three times. For example, 8 is a perfect cube because 2 x 2 x 2 = 8.
Inverse operations of cubing and cube root
Inverse operations of cubing and cube root
Finding the cube root and cubing a number are opposite operations. You can use this relationship to solve equations involving cubes.
Volume of a cube
Volume of a cube
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Surface area of a cube
Surface area of a cube
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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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