## 1.2 Learn Basic Properties and Operations

This lesson will help you learn the basic properties and rules that govern math problem-solving.

### Radicals

A **radical
**
, also called a root, is the opposite of an exponent. Finding a **square root
**
is the opposite of squaring a number. The bracket symbol $$\sqrt {\;} $$ indicates a square root.

### Examples

$${8^2} = 64$$ | 8 squared is 64. |

$$\sqrt {64} = 8$$ | The square root of 64 is 8. |

You may have noticed that –8 could also be the square root of 64 because $$( - 8)( - 8) = 64$$. Most real-life situations require the positive root, but in special situations both roots may be needed. We can show both roots in this way: $$\sqrt {16}
= \pm 4$$, which means “the square root of 16 is *plus or minus* 4.”

A cube root is the opposite of raising a number to the third power. An **index number
**
is written in the angle of the bracket to show which root is meant.

### Examples

$$\sqrt[3]{8} = 2$$ | The cube root of 8 is 2 because $${2^3} = 8$$. | |

$$\sqrt[4]{{625}} = 5$$ | The fourth root of 625 is 5 because $${5^4} = 625$$. |

A cube root can be negative: $$\sqrt { - 27} = - 3$$ because $$( - 3)( - 3)( - 3) = - 27$$.