Understanding the Square Root of the Sum: GMAT Practice Explained

Which of the following is NOT equal to the square root of the sum of two numbers a and b?

• A. (√a) + (√b)
• B. √(a + b)
• C. √a + √b
• D. √(ab)

Answer: (B)

The question is asking for the option that does not equal the square root of the sum of two numbers, a and b. The correct answer, which states that the square root of the sum of a and b is not equal to option B, is accurate. The expression given in option B is √(a + b), which by definition is equal to the square root of the sum of the two numbers. Therefore, this choice represents exactly what the question is asking about and fits as a valid representation. In contrast, the other options can be analyzed as follows: the expression (√a) + (√b) or √a + √b implies that you're taking the square root of a and b individually and then adding those values together. This operation does not yield the same result as taking the square root of their sum, which is why these expressions are not equal to √(a + b). Lastly, √(ab) represents the square root of the product of the two numbers, which is distinctly different and also does not equate to √(a + b). Consequently, the correctness of option B lies in its direct representation of the sum, confirming it as equal to the square root of a plus b, thus marking it as

When prepping for the GMAT, understanding mathematical concepts like square roots can make a significant difference in your test performance. You know what? It’s not just about solving problems; it’s about grasping the underlying principles that will help you breeze through the exam. Let’s dive into a tantalizing question that highlights the difference between the square root of the sum of two numbers, (a) and (b), and other related expressions.

What’s the Question?

Imagine you’re pressed for time and faced with this puzzler: Which of the following is NOT equal to the square root of the sum of two numbers (a) and (b)?

1. (√a) + (√b)

2. √(a + b)

3. √a + √b

4. √(ab)

At first glance, it may seem straightforward, but let’s take a closer look at each option.

Breaking Down the Options

Option B - The Misunderstood One

When you see √(a + b), what do you think? This expression literally represents the square root of the sum of (a) and (b). It means you add (a) and (b) together first, then you find the square root of that sum. So, if we’re doing a quick check, this option stands firm as an accurate representation! It’s equal to what the question is really asking about.

Option A and C - The Sneaky Ones

Now, what about (√a) + (√b)? This is where things get a bit tricky. Here, you’re not summing (a) and (b) first; instead, you’re calculating the square root of each separately and then adding those results. It might sound right, but it’s mathematically off from option B. The same logic applies to √a + √b—both yield different results compared to √(a + b).

Option D - The Mighty Product

Lastly, let’s examine √(ab). This is the square root of the product of (a) and (b). It compounds the values and results in a whole different calculation. So, yeah, you guessed it—it’s not equal to √(a + b) either!

Why This Matters

So why dwell on this specific question? Because the GMAT is all about precision and detail! Understanding how to navigate these expressions not only helps with one question but deepens your grasp of algebraic principles overall.

Being able to differentiate between (√(a + b)), ((√a) + (√b)), and more, can be a game-changer. A strong mathematical foundation enhances your confidence as you tackle GMAT questions, ensuring you’re not just answering but understanding.

Wrap-up: Keep Practicing!

The GMAT’s mathematical section can feel like a sprawling maze. It’s all too easy to get lost in the details. Embracing this analytical approach aids in strengthening your competencies as a test-taker. So keep practicing with these variations on square roots and enjoy the sense of accomplishment that comes with progress. You’ve got this, and you never know; the next time you face a question like this, it may be a breeze!

Feel free to explore more GMAT resources to sharpen those skills, stay tuned for future explanations, and remember: clarity is key!