Solving 52x3÷4+√√441 ÷ 7×3 +5-32 ÷8x12 A Step-by-Step Guide
Hey guys! Ever stumbled upon a mathematical expression that looks like it belongs in a secret code? Well, 52x3÷4+√√441 ÷ 7×3 +5-32 ÷8x12 might just be that code! But fear not, because we're about to crack it wide open. This isn't just about getting the right answer; it's about understanding the journey to the solution. So, buckle up, grab your calculators (or your mental math muscles), and let's dive into this mathematical adventure!
Deciphering the Mathematical Expression
At first glance, the expression 52x3÷4+√√441 ÷ 7×3 +5-32 ÷8x12 might seem intimidating. There's a mix of multiplication, division, square roots, and good old addition and subtraction. But remember, every complex problem can be broken down into simpler, manageable steps. The key here is to follow the order of operations, often remembered by the acronym PEMDAS (or BODMAS, depending on where you learned math). This handy acronym tells us the sequence in which we should tackle the different operations:
- Parentheses (or Brackets)
- Exponents (or Orders)
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Following PEMDAS, we'll navigate through the expression, simplifying it step-by-step until we arrive at the final answer. Think of it like following a map to a hidden treasure – each step brings us closer to our goal. So, let's start our mathematical expedition!
Step 1: Tackling the Square Roots
Our journey begins with the nested square roots: √√441. This might look a bit scary, but it's actually quite straightforward. We need to work from the inside out. First, let's find the square root of 441. If you're familiar with your perfect squares, you'll know that 441 is 21 squared (21 x 21 = 441). So, √441 = 21. Now our expression looks a little friendlier: 52x3÷4+√21 ÷ 7×3 +5-32 ÷8x12.
Next, we need to find the square root of 21. This isn't a perfect square, so we'll get a decimal approximation. Using a calculator, we find that √21 is approximately 4.58. Now, let's update our expression: 52x3÷4+4.58 ÷ 7×3 +5-32 ÷8x12. See? We're already making progress! The expression is becoming less daunting with each step. The key takeaway here is that breaking down complex operations like nested square roots into smaller, manageable steps makes the whole process much easier. It's like eating an elephant – one bite at a time!
Step 2: Division and Multiplication - The Left-to-Right Dance
Now that we've handled the square roots, it's time to tackle the multiplication and division. Remember, PEMDAS tells us to perform these operations from left to right. So, let's start at the beginning of our expression: 52x3÷4+4.58 ÷ 7×3 +5-32 ÷8x12.
First up is 52 x 3, which equals 156. Our expression now reads: 156÷4+4.58 ÷ 7×3 +5-32 ÷8x12. Next, we divide 156 by 4, giving us 39. The expression is slimming down nicely: 39+4.58 ÷ 7×3 +5-32 ÷8x12. Now, we encounter 4. 58 ÷ 7, which is approximately 0.654. Let's plug that in: 39+0.654×3 +5-32 ÷8x12.
Moving along, we have 0.654 x 3, which equals approximately 1.962. Our expression is getting shorter and shorter: 39+1.962 +5-32 ÷8x12. Next in line is the division 32 ÷ 8, resulting in 4. Our ever-evolving expression now looks like this: 39+1.962 +5-4x12. Finally, we have 4 x 12, which equals 48. This leaves us with a much simpler expression: 39+1.962 +5-48. The crucial point here is the methodical approach of performing multiplication and division from left to right. This ensures that we follow the correct order of operations and avoid any mathematical mishaps.
Step 3: Addition and Subtraction - The Final Countdown
We've reached the final stage of our mathematical journey! All that's left is addition and subtraction. Just like with multiplication and division, we'll work from left to right. Our expression currently looks like this: 39+1.962 +5-48.
First, let's add 39 and 1.962, which gives us 40.962. Our expression simplifies to: 40.962 +5-48. Next, we add 40.962 and 5, resulting in 45.962. Now we're down to the wire: 45.962-48. Finally, subtracting 48 from 45.962 gives us -2.038.
So, after all that mathematical maneuvering, we've arrived at our final answer: -2.038. This final step highlights the importance of paying close attention to the signs (positive and negative) when performing addition and subtraction. A small mistake here can throw off the entire calculation. But hey, we made it! We successfully navigated the complex expression and emerged victorious!
The Final Answer and Key Takeaways
So, the final answer to 52x3÷4+√√441 ÷ 7×3 +5-32 ÷8x12 is approximately -2.038. But more than just getting the answer, we've learned some valuable lessons along the way:
- PEMDAS is your friend: Always remember the order of operations (PEMDAS/BODMAS) to ensure you tackle the expression in the correct sequence.
- Break it down: Complex expressions can be intimidating, but breaking them down into smaller, manageable steps makes the process much easier.
- Left to right: When performing multiplication and division (or addition and subtraction), work from left to right.
- Pay attention to signs: Be mindful of positive and negative signs, especially during addition and subtraction.
Why This Matters: The Importance of Order of Operations
You might be thinking,