Predict
Look at eighty-nine minus the quantity thirteen plus seventeen, divided by six, times two cubed.
Which operation comes first in this expression?
Keep thirteen plus seventeen together inside the parentheses.

Model
Calculate grouping first, then powers and square roots.
Multiplication and division have equal priority. Work them from left to right.
Then add and subtract from left to right.
The square root symbol asks for the nonnegative root. The square root of forty-nine is seven.

Work
Inside the parentheses, thirteen plus seventeen is thirty.
Two cubed is eight.
Next calculate thirty divided by six, then multiply by eight.
Thirty divided by six is five. Five times eight is forty.
Finally, eighty-nine minus forty is forty-nine.

Check Result
Try the same lesson check.
Twenty-four divided by the square root of one hundred forty-four.
Then add the quantity twenty-three minus fourteen, squared.
Calculate before the answer appears.
Keep twenty-three minus fourteen together before squaring it.
[Eight-second silent pause to work; the answer remains hidden.]
Twenty-three minus fourteen is nine. Nine squared is eighty-one.
The square root of one hundred forty-four is twelve. Twenty-four divided by twelve is two.
Two plus eighty-one is eighty-three.

Interpret
The order of operations and the scope of grouping determine the result.
Multiplication and division have equal priority, so their left-to-right order matters.
A square-root symbol gives the principal nonnegative root.
Solving a squared equation can also involve a negative solution.