Solving Square Root and Cube Root Equations

Front

What is 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.

Front

What is 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.

Front

How do you solve the equation x² = 16?

Back

To solve x² = 16, take the square root of both sides: x = ±4.

Front

What is the principal square root?

Back

The principal square root is the non-negative square root of a number. For example, the principal square root of 25 is 5.

Front

What is the difference between a square root and a cube root?

Back

A square root finds a number that, when multiplied by itself, gives the original number, while a cube root finds a number that, when multiplied by itself three times, gives the original number.

Front

How do you check if a number is a solution to a square root equation?

Back

Substitute the number back into the original equation and verify if both sides are equal.

Front

What is the square root of 0?

Back

The square root of 0 is 0, since 0² = 0.

Front

What is the cube root of -8?

Back

The cube root of -8 is -2, since (-2)³ = -8.

Front

How do you solve the equation x³ = 27?

Back

To solve x³ = 27, take the cube root of both sides: x = 3.

Front

What is the domain of the square root function?

Back

The domain of the square root function is all non-negative real numbers, as you cannot take the square root of a negative number in the real number system.