Evaluate the expression:
$[3(2+3)-5]+4^2$
To evaluate the expression \([3(2+3)-5]+4^2\), we must follow the standard order of operations (often known as PEMDAS or BODMAS). This rule dictates that we perform operations in the following order: Parentheses, Exponents, Multiplication and Division (from left to right), and finally Addition and Subtraction (from left to right). Our expression has nested groupings and an exponent, so we will address them sequentially.
First, we focus on the innermost part of the expression: the parentheses \((2+3)\).
Performing the addition inside:
\[2 + 3 = 5\]
Substituting this value back into the expression gives us:
\[[3(5) - 5] + 4^2\]
Next, we simplify the expression inside the square brackets \([3(5) - 5]\). According to the order of operations, multiplication comes before subtraction.
Multiplying:
\[3 \times 5 = 15\]
Now subtracting:
\[15 - 5 = 10\]
So the entire bracketed expression simplifies to \(10\).
Now we handle the exponential term \(4^2\).
Calculating the square:
\[4^2 = 4 \times 4 = 16\]
Substituting our results back into the full expression:
\[10 + 16\]
Performing the final addition:
\[10 + 16 = 26\]
Comparing this result to the given options, we find that the correct choice is \(b\). The final value is \(\boxed{26}\).
Order of operations is fundamental in everyday life, especially in fields like finance and engineering. For example, if you are calculating the total cost of an order where you have a discount and shipping fees, you need to calculate the items' total price first (often inside parentheses), then apply the discount (multiplication), and finally add the shipping fee (addition). Understanding these steps ensures that calculations are performed correctly, leading to accurate budgets and project plans.