Solving Square and Cube Root Equations

Front

What is the definition of a square root?

Back

A square root of a number x is a number y such that y² = x. For example, the square root of 9 is 3, since 3² = 9.

Front

What is the definition of a cube root?

Back

A cube root of a number x is a number y such that y³ = x. For example, the cube root of 27 is 3, since 3³ = 27.

Front

How do you solve the equation x² = a?

Back

To solve the equation x² = a, take the square root of both sides: x = ±√a.

Front

How do you solve the equation x³ = a?

Back

To solve the equation x³ = a, take the cube root of both sides: x = ∛a.

Front

What is the principal square root?

Back

The principal square root of a non-negative number x is the non-negative number y such that y² = x.

Front

What is the relationship between square roots and perfect squares?

Back

A perfect square is a number that can be expressed as the square of an integer. The square root of a perfect square is always an integer.

Front

What is the relationship between cube roots and perfect cubes?

Back

A perfect cube is a number that can be expressed as the cube of an integer. The cube root of a perfect cube is always an integer.

Front

How can you express the square root of a product?

Back

The square root of a product can be expressed as the product of the square roots: √(a*b) = √a * √b.

Front

How can you express the cube root of a product?

Back

The cube root of a product can be expressed as the product of the cube roots: ∛(a*b) = ∛a * ∛b.

Front

What is the formula for the square root of a fraction?

Back

The square root of a fraction can be expressed as the square root of the numerator divided by the square root of the denominator: √(a/b) = √a / √b.