Solving Math Expression D) (1-3 ²): (-3 + 1) + (-5² + 6.3). 2-√6.√24

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Hey guys! Math can sometimes feel like navigating a maze, but with a systematic approach, even the trickiest-looking expressions can be conquered. Today, we're diving into a fascinating mathematical puzzle: D) (1-3 ²): (-3 + 1) + (-5² + 6.3). 2-√6.√24. This expression involves a mix of operations – exponents, division, addition, multiplication, and square roots – which means we need to be extra careful with the order of operations. Don't worry, we'll break it down step-by-step, making sure every part is crystal clear. Our main goal here is not just to arrive at the correct answer, but also to understand why we're doing each step. Understanding the underlying principles is key to tackling similar problems in the future. So, grab your thinking caps, and let's get started on this mathematical adventure!

Unraveling the Expression: A Journey Through Order of Operations

To successfully solve this mathematical puzzle, we need to become masters of the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This order dictates the sequence in which we perform calculations to ensure we arrive at the correct answer. Let’s dive deep into why PEMDAS is so important and how it guides us through complex expressions. Imagine if we didn't have a set order – we might end up with wildly different answers depending on which operation we performed first! That's why mathematicians established this universal rule, ensuring consistency and clarity in mathematical calculations.

Step 1: Taming the Parentheses

The first step in our mathematical journey is to tackle the parentheses. Within the expression D) (1-3 ²): (-3 + 1) + (-5² + 6.3). 2-√6.√24, we have three sets of parentheses to address. Let's break them down individually:

  • (1-3 ²): Inside this parenthesis, we first encounter an exponent. Remember, exponents come before subtraction in the order of operations. So, we calculate 3² (3 squared), which is 3 * 3 = 9. Now we have (1 - 9), which simplifies to -8.
  • (-3 + 1): This one is straightforward. Adding -3 and 1 gives us -2.
  • (-5² + 6.3): Here, we again encounter an exponent. -5² means -(5*5) which equals -25. Next, we add 6.3 to -25. This gives us -18.7

By carefully addressing the parentheses first, we've simplified the expression and paved the way for the next steps.

Step 2: Exponents - The Power Players

We've already dealt with the exponents within the parentheses, so this step is already incorporated into our previous calculations. Remember, exponents tell us how many times to multiply a number by itself. For example, 3² means 3 multiplied by itself (3 * 3), which equals 9. Understanding exponents is crucial for simplifying expressions and solving equations.

Step 3: Multiplication and Division - A Balancing Act

Now, we move on to multiplication and division. These operations have equal priority in the order of operations, so we perform them from left to right. In our simplified expression, we have the following multiplications and divisions:

  • (-8) : (-2): Dividing -8 by -2 results in a positive 4. Remember, a negative divided by a negative is a positive.
  • (-18.7) . 2: Multiplying -18.7 by 2 gives us -37.4.
  • -√6.√24: We'll tackle this part later, as it involves square roots, which we'll address in the next step.

By performing multiplication and division in the correct order, we continue to simplify the expression, bringing us closer to the final answer.

Step 4: Unveiling the Square Roots

Our next challenge involves square roots. We have the term -√6.√24 to simplify. Remember, the square root of a number is a value that, when multiplied by itself, gives the original number. To simplify this, we can use a handy property of square roots: √(a) * √(b) = √(a * b). Applying this to our expression, we get:

  • -√6.√24 = -√(6 * 24)
  • -√(6 * 24) = -√144
  • -√144 = -12 (Since the square root of 144 is 12)

By understanding the properties of square roots, we've successfully simplified this part of the expression.

Step 5: Addition and Subtraction - The Grand Finale

Finally, we arrive at the last step: addition and subtraction. Like multiplication and division, these operations have equal priority, so we perform them from left to right. Our expression has now been simplified to:

  • 4 + (-37.4) - 12

Let's perform the addition and subtraction:

  • 4 + (-37.4) = -33.4
  • -33.4 - 12 = -45.4

And there you have it! After carefully following the order of operations, we've arrived at the final answer: -45.4.

The Final Verdict: D) (1-3 ²): (-3 + 1) + (-5² + 6.3). 2-√6.√24 = -45.4

So, after our mathematical journey through parentheses, exponents, multiplication and division, and finally, addition and subtraction, we've successfully solved the expression D) (1-3 ²): (-3 + 1) + (-5² + 6.3). 2-√6.√24. The answer is -45.4. Remember, the key to tackling complex mathematical problems is to break them down into smaller, manageable steps and to always adhere to the order of operations. By doing so, you can conquer even the most intimidating-looking expressions!

I hope this step-by-step explanation has been helpful. Math might seem daunting at times, but with practice and a clear understanding of the rules, you can become a math whiz! Keep practicing, keep exploring, and most importantly, keep enjoying the world of mathematics!