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.