Resolver
a) $\sqrt{25}-3 \cdot(3-2)$
Answer (2)
To evaluate the expression 25 − 3 ⋅ ( 3 − 2 ) , we first solve the parentheses, then compute the square root, perform the multiplication, and finally the subtraction. The final answer is 2 .
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Evaluate the expression inside the parentheses: ( 3 − 2 ) = 1 .
Calculate the square root: 25 = 5 .
Perform the multiplication: 3 ⋅ 1 = 3 .
Perform the subtraction: 5 − 3 = 2 . The final answer is 2 .
Explanation
Understanding the problem We are asked to evaluate the expression 25 − 3 ⋅ ( 3 − 2 ) . To do this, we will follow the order of operations (PEMDAS/BODMAS).
Evaluating parentheses First, we evaluate the expression within the parentheses: ( 3 − 2 ) = 1 .
Evaluating square root Next, we evaluate the square root: 25 = 5 .
Performing multiplication Now, we perform the multiplication: 3 ⋅ ( 3 − 2 ) = 3 ⋅ 1 = 3 .
Performing subtraction Finally, we perform the subtraction: 25 − 3 ⋅ ( 3 − 2 ) = 5 − 3 = 2 .
Final answer Therefore, the value of the expression is 2.
Examples
Understanding order of operations is crucial in many real-life scenarios, such as calculating expenses or understanding scientific formulas. For example, if you are calculating the total cost of items with discounts and taxes, following the correct order ensures you get the accurate final amount. Imagine you buy an item for $25, get a discount of $3 multiplied by the quantity (3-2 = 1), the final price is $25 - 3*1 = $22. This principle applies in various fields, from personal finance to engineering.
