The order of operations outlines an order we should follow to evaluate expressions with multiple operations. We often use the acronym PEMDAS to remember the order of operations:
It is important to remember that the "parentheses" part of the order of operations includes grouping symbols, such as braces or brackets. There are several types of operations that act as grouping symbols. This means that they are operations, but need to be considered first in the order of operations, because they also enclose other expressions in parentheses, even though they might not be visible.
In this lesson, we will see three operations that act as grouping symbols: fraction bars, absolute value bars, and the radical symbol.
If we have a fraction, the entire numerator and the entire denominator must be evaluated before we reduce the fraction. In these cases, we can simplify in both the numerator and denominator at the same time.

Exponent in the numerator, divide in denominator  

Multiply in the numerator, subtract in the denominator  

Add the opposite to simplify numerator, denominator is done  

Reduce, divide  

Our Solution 
Another type of grouping symbol that also has an operation with it is absolute value. When we have an absolute value, we will evaluate everything inside the absolute value bars, just as if it were a normal parentheses. Then once the inside is completed, we will take the absolute value, or distance from zero, to make sure the number is nonnegative.

Evaluate absolute first, exponents  

Add inside absolute values  

Evaluate absolute values  

Multiply left to right  

Finish multiplying  

Add left to right  

Add  

Our Solution 
Expressions can be underneath radical symbols, just like they can be in numerators, denominators, or within absolute value bars. When an expression is underneath a radical, this groups the expression together, and acts as a grouping symbol. This means we must fully evaluate the expression underneath the radical sign, before moving on to other operations in the order of operations. Let's take a look at an example:

The radical sign groups the expression  

Multiply by  

Add 5  

Evaluate the square root  

Our Solution 