Understanding Cubes
Understanding cubes is a Grade 7 math concept in Big Ideas Math Advanced 2, Chapter 7: Real Numbers and the Pythagorean Theorem, where the exponent 3 is called cubed because it relates to the volume of a cube. The volume of a cube with edge length s equals s cubed, connecting geometry to algebra. For example, 5 cubed means 5 times 5 times 5, which equals 125.
Key Concepts
The exponent 3 is used frequently, so it has a special name.
Instead of reading $5^3$ as "5 raised to the third power," we say "5 cubed.".
Common Questions
What does cubed mean in math?
Cubed means raising a number to the third power, or multiplying it by itself three times. For example, 4 cubed means 4 times 4 times 4, which equals 64.
Why is the exponent 3 called cubed?
The term cubed comes from geometry: the volume of a cube with edge length s equals s times s times s, written as s cubed. This connects the operation to the three dimensions of a physical cube.
How is cubing a number related to cube roots?
Cubing a number and taking a cube root are inverse operations. If 3 cubed equals 27, then the cube root of 27 is 3.
What textbook covers understanding cubes in Grade 7?
Big Ideas Math Advanced 2, Chapter 7: Real Numbers and the Pythagorean Theorem covers cubes and cube roots as foundational concepts.