# Definition of Exponents & Radicals

## What does it mean?

### Definitions:

From Wolfram MathWorld:

Exponents - An exponent is the power p in an expression of the form $$a^p$$ The process of performing the operation of raising a base to a given power is known as exponentiation. (where a ≠0)

Radicals - The symbol $$\sqrt[n]{x}$$ used to indicate a root is called a radical and is therefore read "x radical n," or "the nth root of x." In the radical symbol, the horizontal line is called the vinculum, the quantity under the vinculum is called the radicand, and the quantity n written to the left is called the index.

The special case $$\sqrt[2]{x}$$ is written $$\sqrt{x}$$ and is called the square root of x. $$\sqrt[3]{x}$$ is called the cube root.

MORE:

Radical - The √ symbol that is used to denote square root or nth roots.

Radical Expression - A radical expression is an expression containing a square root.

## What does it look like?

A general example to help you recognize patterns and spot the information you're looking for

Some examples of radical expressions are: $$\sqrt{5}, 3\sqrt{y} + 1, \sqrt[6]{15}, and 5 \pm \sqrt[2]{9}$$ Evaluate the radical expression: $$\frac{8 + 2\sqrt{b}}{a}$$ when a = 2 and b = 4. $$\frac{8 + 2\sqrt{b}}{a}$$ $$= \frac{8 + 2\sqrt{4}}{2}$$ $$= \frac{8 + 2(2)}{2}$$ $$= \frac{12}{2}$$ $$= 6$$

## You'll use it...

It’s used in construction, like finding amount of materials for construction, etc.

## Video

### How to Rationalize a Denominator

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Length: 10:18

## Video

### Simplifying Expressions with Exponents

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Length: 3:49

## Video

### Simplifying Expressions with Exponents 2

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Length: 2:30

## Video

### Simplifying Rational Expressions 3

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Length: 2:38

## Video

### Fractional Exponent Expressions 2

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Length: 7:32

## Video

### Zero, Negative, and Fractional Exponents

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Length: 14:04

## Video

### Exponent Properties 1

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Length: 2:36

## Video

### Exponent Properties 2

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Length: 5:12