**Roots** are sort of like the opposites of powers.

The **square root** of , written as , means "what number times itself gives an answer of ?"

- 3 squared, or 3 to the second power () is
- So, the square root of is

The **cube root** of , written as , means "what number times itself *three times* is ?"

- 2 cubed, or 2 to the third power () is
- So, the cube root of is

**Roots can also be written as exponents.**

The square root can be written as something raised to the power of , while a cube root is written as something raised to the power of . For example, can be written as .

- Since is , = .

**Look Out**: Order of operation (PEMDAS) always applies, so when there is an operation to simplify underneath the root symbol, simplify the operation, then take the root.

**You cannot take the square root of a negative number.**

A number times itself could never be negative. So, there is no answer to the problem , since and too.

However, *you can take the cube root of a negative number*.

The cube root of is (), since .

Roots Example 1

Roots Example 2

Roots Example 3

Roots Example 4

Roots Exercise 1

Roots Exercise 2

Roots Exercise 3

Roots Exercise 4

Roots Exercise 5