Solving E = 15/√9+3(√64+√64) A Step-by-Step Guide

Hey guys! Ever stumbled upon a math problem that looks like it's written in another language? Well, today we're tackling one of those head-scratchers together: E = 15/√9+3(√64+√64). Don't worry, it's not as intimidating as it looks. We're going to break it down step-by-step, so you'll not only understand the solution but also the why behind each step. Think of this as your friendly guide to conquering complex equations! We will begin by dissecting each component, making sure everyone, regardless of their math background, can follow along. So, buckle up, grab your thinking caps, and let's dive into the fascinating world of mathematical problem-solving. We'll go from confusion to clarity, turning this seemingly complex equation into a piece of cake. Trust me, by the end of this article, you'll be looking at similar equations with a newfound confidence. Let's get started!

Unraveling the Basics: A Step-by-Step Breakdown

Okay, let's get down to business! Our mission is to solve for E in the equation E = 15/√9+3(√64+√64). The key to tackling any mathematical problem is to break it down into smaller, more manageable steps. We're going to use the good ol' order of operations (PEMDAS/BODMAS) as our roadmap. Remember that? Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This is our golden rule, our guiding star in this mathematical journey. Ignoring this order is like trying to build a house without a blueprint – chaos will ensue! So, we'll stick to it religiously. We'll start with the innermost parts of the equation, gradually working our way outwards. This methodical approach ensures we don't miss anything and keeps our calculations nice and tidy. Think of it as peeling an onion, layer by layer, until we get to the core. Each step we take will bring us closer to the final answer, and more importantly, to a deeper understanding of the equation itself. Ready to peel some mathematical onions? Let's do it!

Diving into Parentheses: Simplifying (√64+√64)

Let's kick things off by focusing on the heart of our equation, the parentheses: (√64+√64). Inside these brackets lies the key to unlocking the rest of the problem. Remember, parentheses are like VIP sections in a math equation – we gotta deal with them first! The first thing we spot inside is the square root symbol, √. Now, what does that mean? Simply put, the square root of a number is a value that, when multiplied by itself, gives you the original number. For instance, the square root of 9 is 3 because 3 * 3 = 9. Make sense? So, what's the square root of 64? Think about it… What number times itself equals 64? Bingo! It's 8 (because 8 * 8 = 64). So, √64 confidently steps out as 8. Now, our expression inside the parentheses looks a lot simpler: (8 + 8). This is a piece of cake, right? Adding 8 and 8 gives us 16. So, (√64+√64) gracefully transforms into 16. We've conquered the parentheses! This is a huge win, guys! We've taken a big chunk out of the equation and made it much less intimidating. You're doing great! Let's carry this momentum forward and tackle the next step with the same confidence and clarity.

Tackling the Square Root: Simplifying √9

Alright, with the parentheses tamed, let's turn our attention to another square root lurking in our equation: √9. Remember what we learned about square roots? We're looking for a number that, when multiplied by itself, gives us 9. Think of it like a mathematical puzzle – what number fits the bill? The answer is 3, because 3 * 3 = 9. So, √9 confidently simplifies to 3. See how we're chipping away at the equation, making it more and more manageable? Each simplification is a victory! Now, our equation is starting to look a lot friendlier. We've taken another step closer to unraveling the mystery of E. We've handled the parentheses, we've conquered another square root – you're on fire! Don't let the seemingly complex nature of the original equation fool you. By breaking it down into these bite-sized pieces, we're making progress with every step. Let's keep this momentum going and see what other mathematical goodies await us.

Multiplication Magic: Solving 3(16)

Now that we've simplified the square roots and the parentheses, it's time to tackle the multiplication. Our equation now looks like this: E = 15/3 + 3(16). Notice the 3 right next to the (16)? In math, when you see a number snuggled up against a parenthesis like that, it means multiplication. So, we need to figure out what 3 times 16 is. You can do this the old-fashioned way with some long multiplication, or if you're feeling confident, you can break it down in your head. Think of it as 3 times 10 (which is 30) plus 3 times 6 (which is 18). Add those together, and what do you get? That's right, 48! So, 3(16) transforms into 48. See how far we've come? We're taking a complex-looking equation and turning it into something much simpler, step by step. Multiplication can sometimes feel a bit intimidating, but with practice, it becomes second nature. And remember, there are always different ways to approach multiplication, so find the method that clicks best for you. Now, let's take a deep breath and admire our progress. We've conquered the parentheses, the square roots, and now the multiplication. What's next? Let's keep unraveling this mathematical mystery!

Division and Addition: Finishing the Equation

We're in the home stretch now, guys! Our equation has slimmed down to E = 15/3 + 48. We've conquered the parentheses, the square roots, and the multiplication. Now, we're left with division and addition. Remember our golden rule, PEMDAS/BODMAS? It tells us to tackle division before addition. So, let's divide 15 by 3. What do we get? That's right, 5! So, 15/3 elegantly simplifies to 5. Now, our equation looks even simpler: E = 5 + 48. This is the final countdown! We're just one step away from solving for E. All that's left to do is add 5 and 48. And the answer is… 53! So, E = 53. We did it! We cracked the code! We took a seemingly complex equation and, by breaking it down step-by-step, we found the solution. Give yourselves a pat on the back, guys. You've earned it! This final step, the addition, is the satisfying culmination of all our hard work. It's the moment where all the pieces fall into place and the answer reveals itself. But more than just finding the answer, we've learned a valuable lesson about problem-solving: break it down, stay organized, and follow the rules. And now, you can look at equations like this with a newfound confidence, knowing that you have the tools and the knowledge to conquer them.

Final Answer: E = 53

And there you have it! The solution to our equation E = 15/√9+3(√64+√64) is E = 53. We've journeyed through the world of parentheses, square roots, multiplication, division, and addition, all guided by the trusty order of operations. We started with a problem that might have seemed daunting, but by breaking it down into smaller, more manageable steps, we arrived at the answer with clarity and confidence. Remember, guys, math isn't about magic or innate talent; it's about understanding the rules and applying them systematically. And that's exactly what we did today. We didn't just find the answer; we understood why the answer is what it is. That's the real victory here. So, the next time you encounter a mathematical challenge, remember our journey together. Remember the power of breaking things down, the importance of following the order of operations, and the satisfaction of arriving at the solution. Keep practicing, keep exploring, and keep that mathematical curiosity alive! You've got this!