## 1.2 Learn Basic Properties and Operations

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

A radical , also called a root, is the opposite of an exponent. Finding a 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. Anis 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 $$( - 3)( - 3)( - 3) = - 27$$.