Squares, Cubes, Square Roots, and Cube Roots

Front

What is the formula for the volume of a cube?

Back

The volume V of a cube with side length s is given by the formula V = s³.

Front

If the volume of a cube is 64 cubic units, what is the length of one side?

Back

The length of one side is 4 units, since 4³ = 64.

Front

What are perfect squares?

Back

Perfect squares are numbers that can be expressed as the square of an integer. Examples include 0, 1, 4, 9, 16, 25, etc.

Front

List three perfect squares.

Back

9, 81, 100.

Front

What is the relationship between squaring a number and taking its square root?

Back

Squaring a number and taking its square root are inverse operations. If x is a non-negative number, then √(x²) = x.

Front

What is the equation for 'Two cubed is equal to the square root of x'?

Back

The equation is 2³ = √x, which simplifies to 8 = √x.

Front

What is a cube root?

Back

The cube root of a number x is a number y such that y³ = x. It is denoted as ∛x.

Front

Which of the following is irrational: √50, 4, or 9?

Back

√50 is irrational because it cannot be expressed as a fraction of two integers.

Front

What is the value of 3 squared?

Back

3 squared is 9, since 3² = 9.

Front

What is the value of 5 cubed?

Back

5 cubed is 125, since 5³ = 125.