Solving Mathematical Expressions √64 + 6 × 5 - 20 ÷ 2 A Step-by-Step Guide
Solve the math problem: √64 + 6 × 5 - 20 ÷ 2
Introduction
In this article, we will delve into the step-by-step process of solving the mathematical expression √64 + 6 × 5 - 20 ÷ 2. This problem involves various arithmetic operations, including square roots, multiplication, subtraction, and division. By understanding the order of operations and applying it correctly, we can arrive at the accurate solution. This comprehensive guide aims to provide a clear and detailed explanation, ensuring that readers can confidently solve similar mathematical problems in the future. Let’s embark on this mathematical journey and unravel the solution together.
Breaking Down the Expression
To accurately solve the expression √64 + 6 × 5 - 20 ÷ 2, it is crucial to understand the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). PEMDAS dictates the sequence in which operations must be performed to ensure a consistent and correct result. We'll break down the expression into manageable parts, adhering to this order. First, we address the square root, then multiplication and division from left to right, and finally, addition and subtraction, also from left to right. This methodical approach will allow us to tackle the problem systematically, minimizing errors and clarifying each step involved. By following this structure, we transform a potentially confusing expression into a series of straightforward calculations.
1. Square Root: √64
The first step in solving the expression is to address the square root. The square root of 64 is a number that, when multiplied by itself, equals 64. In this case, that number is 8, since 8 × 8 = 64. Understanding square roots is foundational in mathematics, as they often appear in various algebraic and geometric problems. Recognizing perfect squares like 64 simplifies calculations and builds a strong base for more complex mathematical operations. Thus, we can replace √64 with 8 in our expression, making the next steps clearer and more straightforward. This initial simplification is a key component in solving the overall expression.
2. Multiplication: 6 × 5
Following the order of operations, after addressing the square root, we move on to multiplication and division, working from left to right. Here, we encounter the multiplication operation: 6 multiplied by 5. This straightforward calculation results in 30. Multiplication is a fundamental arithmetic operation, and its accurate execution is crucial for solving mathematical expressions. With this step completed, we reduce the complexity of the expression, making it easier to manage the remaining operations. The result, 30, will be used in the subsequent steps as we continue to break down the problem and move closer to the final solution. This methodical progression ensures accuracy and clarity in our calculations.
3. Division: 20 ÷ 2
Next, we address the division operation in the expression. We have 20 divided by 2, which equals 10. Division is another fundamental arithmetic operation that must be performed accurately to solve mathematical problems. Just like multiplication, division helps us simplify the expression and move closer to the final answer. Now that we've performed this division, we can replace 20 ÷ 2 with 10 in our expression. This step-by-step approach ensures that we handle each operation in the correct order, minimizing errors and making the overall calculation more manageable. With the division completed, we are now ready to perform the remaining addition and subtraction operations.
4. Addition and Subtraction: 8 + 30 - 10
Having completed the square root, multiplication, and division, we now focus on the addition and subtraction operations. According to the order of operations, we perform these from left to right. Starting with 8 + 30, we get 38. Then, we subtract 10 from 38, resulting in 28. Addition and subtraction are essential arithmetic operations, and handling them in the correct sequence is vital for arriving at the correct solution. This final step consolidates the results of the previous operations, bringing us to the ultimate answer. By following the order of operations meticulously, we ensure that the solution is both accurate and reliable. The process highlights the importance of structured calculation in mathematics.
Final Answer
After meticulously following the order of operations and performing each calculation step by step, we arrive at the final answer. The expression √64 + 6 × 5 - 20 ÷ 2 simplifies to 8 + 30 - 10, which further simplifies to 38 - 10, and finally, to 28. Therefore, the solution to the given mathematical expression is 28. This result underscores the significance of adhering to the correct sequence of operations to ensure accuracy in mathematical calculations. By breaking down the problem into smaller, manageable steps, we can confidently tackle complex expressions and arrive at the correct solution.
Conclusion
In summary, solving the mathematical expression √64 + 6 × 5 - 20 ÷ 2 requires a systematic approach, primarily following the order of operations (PEMDAS). We first addressed the square root, then multiplication and division from left to right, and finally, addition and subtraction, also from left to right. Each step was meticulously executed to ensure accuracy. The square root of 64 is 8, 6 multiplied by 5 is 30, and 20 divided by 2 is 10. The expression then became 8 + 30 - 10, which simplifies to 28. The final answer, 28, illustrates the importance of order in mathematical operations. By understanding and applying these principles, anyone can confidently solve similar problems, reinforcing their mathematical skills and problem-solving abilities. This step-by-step methodology not only aids in finding the correct answer but also fosters a deeper understanding of mathematical concepts.