## 1.2 Learn Basic Properties and Operations

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

### Order of Operations

In this example, a radical is used as a grouping symbol. Remember that a radical, or root, is part of the second step in the order of operations.

### Example

Find the value of the expression: $$\sqrt {6 + 10} \,\, + \,2\,\,\cdot \,\,{3^2}$$

Step 1 |
Do the operation in the radical first. | $$\begin{array}{l}\;\;\;\,\sqrt {6 + 10} \,\, + \,2\,\,\cdot \,\,{3^2}\\ = \sqrt {16} + 2\,\,\cdot \,\,{3^2}\\ = 4 + 2\,\,\cdot \,\,9\\ = 4 + 18\\ = 22\end{array}$$ |

Step 2 |
Evaluate the root $$\sqrt {16} $$ and the exponent $${3^2}$$. | |

Step 3 |
Multiply: $$2\,\,\cdot \,\,9$$ | |

Step 4 |
Add: $$4 + 18$$ |

**Answer**$$\sqrt {6 + 10} \,\, + \,2\,\,\cdot\,\,{3^2} = 22$$

You won’t always need every step in the order of operations, but it’s a good idea to think through the steps each time you evaluate an expression to make sure your result is the correct one.