Radical Expressions

Front

What is a radical expression?

Back

A radical expression is an expression that includes a root, such as a square root, cube root, etc. It is typically written in the form of √x or n√x.

Front

How do you simplify a radical expression?

Back

To simplify a radical expression, factor the number under the radical into its prime factors, and then simplify by taking out pairs of factors for square roots, triplets for cube roots, etc.

Front

What does it mean to have no real roots in an equation?

Back

An equation has no real roots when the expression under the radical is negative, meaning that the square root of a negative number is not defined in the set of real numbers.

Front

What is the difference between rationalizing the denominator and simplifying a radical expression?

Back

Rationalizing the denominator involves eliminating radicals from the denominator of a fraction, while simplifying a radical expression focuses on reducing the expression itself.

Front

What is the square root of a number?

Back

The square root of a number x is a value that, when multiplied by itself, gives x. It is denoted as √x.

Front

What is the cube root of a number?

Back

The cube root of a number x is a value that, when multiplied by itself three times, gives x. It is denoted as ∛x.

Front

How do you add or subtract radical expressions?

Back

To add or subtract radical expressions, combine like terms. This means that the radicands (the numbers under the radical) must be the same.

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, 16, and 25 are perfect squares.

Front

What is the process of simplifying a radical expression with a variable?

Back

To simplify a radical expression with a variable, apply the same rules as with numbers, factoring the variable and taking out pairs of the variable.

Front

What is the principle of adding and subtracting radicals?

Back

The principle states that you can only add or subtract radicals if they have the same index and radicand.