# Simplifying numerical radical expressions

4 videos

3 skills

In this tutorial you will simplify numerical expressions with radicals by removing all factors that are perfect squares from inside the radical.

### Simplify numerical radical terms

PRACTICE PROBLEMS

Simplify numerical radical terms by removing all factors that are perfect squares from inside the radical.

### How to simplify a sum of radical terms (example)

VIDEO
4:41 minutes

Sal shows how to group like terms to add and simplify radical terms, by simplifying the expression √(2x^2)+4√8+3√(2x^2)+√8.

### How to simplify a difference of radical terms (example)

VIDEO
5:45 minutes

Sal shows how to group like terms to subtract and simplify radical terms, by simplifying the expression 4∜(81x^5)-2∜(81x^5)-√(x^3).

### Add, subtract, multiply, and divide numerical radical terms

PRACTICE PROBLEMS

Practice simplifying radical expressions with two terms.

### How to rationalize a radical denominator (example)

VIDEO
10:18 minutes

Sal shows how to manipulate expressions like 1/√2 and 12/(2-√5) so there's no radical in the denominator. This is called "rationalizing the denominator."

### How to rationalize a radical denominator in a variable expression (example)

VIDEO
4:58 minutes

Sal shows how to rationalize the denominator of the expression (16+2x^2)/(√8).

### Simplify numerical radical expressions with multiple terms

PRACTICE PROBLEMS

Practice simplifying expressions with multiple radical terms combined by addition, subtraction, multiplication, and/or division.