Mastering Square Roots: Simplifying √108 Made Easy

Have you ever stared at a square root and thought, "What even is this?" If you’re looking to brush up on your math skills—especially if you're prepping for the Kaplan Nursing Entrance Exam—understanding how to simplify expressions like the square root of 108 can be a game-changer. Let's break it down, step by step!

So, what's the simplified form of √108? The options might look tricky at first glance:

• A. 3√3
• B. 6√3
• C. 2√27
• D. 3√12

But guess what? The right answer is B: 6√3. Curious about how we got there? Let’s dive in!

First things first, before we can simplify √108, we need to look at its prime factors. The prime factorization of 108 is 2 × 2 × 3 × 3 × 3, or to put it simply in exponential form, (2^2 \times 3^3). If you've got a good grasp of multiplication tables, you might even pause and think about the efficiency of these little prime flavor elements—fascinating, right?

Now, when it comes to simplifying square roots, here’s where the magic happens. For every pair of identical prime factors, you can take one of those factors outside the square root.

Let's break it down:

1. From (2^2), we take out one 2. Hooray, you’ve got a “2” for your simplified form!
2. For (3^3), we can extract one complete pair of 3s. That leaves us with one 3 inside to juggle, making it a little more interesting.

So how does it all come together? Here's the math lineage: [ \sqrt{108} = \sqrt{2^2 \times 3^3} = 2 \times 3 \times \sqrt{3} ] Simplifying that gets us: [ = 6\sqrt{3} ]

There you have it! The simplified form of (\sqrt{108}) is 6√3. It’s like uncovering the hidden jewel within a chunk of rock—a satisfying feeling!

Now, you might be thinking, “Why does this matter to me?” Well, if you’re gearing up for exams, particularly in nursing, this knowledge is crucial. You’ll encounter similar math challenges that require a solid grasp of simplification and algebraic fundamentals. Plus, knowing how to simplify can save you valuable time during exams.

And let's not overlook the beauty of math itself. It’s not just numbers on a page; it’s a language that helps us understand the world around us. Whether you’re measuring medication dosages or calculating patient stats, these skills are directly applicable. So while it may seem tedious at times, every problem solved is one step closer to not just excelling in the Kaplan Nursing Entrance Exam, but in your future career.

Feeling confident yet? Remember, the key lies in practice. Keep those prime factors close, simplify square roots often, and embrace every opportunity to master the art of numbers. Math might not always seem like your best friend, but with a little patience and practice, it can definitely become an ally.

So keep an eye out for more practice problems, and don’t hesitate to revisit these strategies! With tools in your toolkit like the simplification of √108, you’ll be ready to tackle whatever mathematical challenges come your way.