Simplifying: What Is (√2 / 2) + (√2 / 2)?

Hey guys! Let's dive into a common math problem that often pops up. We're going to break down how to solve the expression (√2 / 2) + (√2 / 2). This might seem a little intimidating at first if you're not used to dealing with square roots, but trust me, it's pretty straightforward. We'll walk through it step by step, so you can totally understand it. Understanding the fundamentals of how to solve this kind of math problem is super important, especially if you're studying for a math exam. Whether you're a math whiz or just trying to brush up on your skills, this explanation is for you. We'll start with the basics, break down the expression, and end up with the simplified answer. Let's get started!

Understanding the Basics: Square Roots and Fractions

Alright, before we get to the actual problem, let's quickly recap some basic math concepts. First up, square roots. A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 (written as √9) is 3 because 3 * 3 = 9. In our problem, we have √2, which is the square root of 2. Unlike √9, √2 is an irrational number, meaning it can't be expressed as a simple fraction, and its decimal representation goes on forever without repeating. But don't let that freak you out; we can still work with it!

Next, let's talk about fractions. A fraction represents a part of a whole. In our expression, we have fractions where the numerator (the top number) is √2, and the denominator (the bottom number) is 2. Remember, when adding fractions, if they have the same denominator, you just add the numerators and keep the denominator the same. This is key to solving our problem.

Now, let's move on to the actual calculation. Keep these concepts in mind; they will become essential as we go along. Getting comfortable with these basics makes the math a lot easier to grasp. So, square roots are numbers that, when multiplied by themselves, equal the original value, and fractions represent a part of a whole. We're all set to solve the expression!

Breaking Down the Expression: (√2 / 2) + (√2 / 2)

Okay, let's get down to business and solve (√2 / 2) + (√2 / 2). The great thing about this problem is that both fractions have the same denominator: 2. This makes our job a lot easier. As mentioned earlier, when you're adding fractions with the same denominator, you simply add the numerators and keep the denominator. In this case, our numerators are both √2.

So, we add √2 + √2. When you add the same square root to itself, it's like saying 1√2 + 1√2, which equals 2√2. So, our new numerator is 2√2. The denominator stays the same, which is 2. Therefore, our expression becomes (2√2) / 2. This is the first main step in simplifying the expression. It's really that simple.

So, (√2 / 2) + (√2 / 2) simplifies to (2√2) / 2. Now we are ready to take it one step further. Now that we've added the fractions, let's simplify further to get our final answer. It is quite an easy process if you follow these steps. Remember, in math, simplifying often means making the expression as concise as possible. The next step is super important to get the correct answer.

Simplifying to the Answer: (2√2) / 2

Great, we've got (2√2) / 2, and now we need to simplify this fraction. Notice that both the numerator and the denominator have a common factor of 2. We can divide both the numerator and the denominator by 2. When you divide 2√2 by 2, you're essentially canceling out the 2 in the numerator and the 2 in the denominator.

This leaves us with just √2. Therefore, the simplified form of (2√2) / 2 is √2. And that's our final answer! So, (√2 / 2) + (√2 / 2) equals √2. Easy peasy, right?

Now you know how to simplify the expression! If you have a calculator, you can find that √2 is approximately 1.414, but often, the most accurate way to leave the answer is as √2. Always check the instructions or any guidelines you might have. You may need to leave the answer in the simplest form, which is √2, or use a calculator to find a decimal approximation. That's up to the question, and the method is still the same.

Recap and Conclusion

So, let's quickly recap what we've learned, guys. We started with the expression (√2 / 2) + (√2 / 2). We reviewed the basics of square roots and fractions. We learned that fractions with the same denominator can be added by adding their numerators. We saw that (√2 / 2) + (√2 / 2) simplifies to (2√2) / 2. Finally, we simplified (2√2) / 2 to √2, our final answer.

Hopefully, this explanation has made the process super clear for you, and now you understand how to solve similar problems. Remember, math is all about practice. The more you work through problems, the more comfortable you'll become. So, keep practicing, and don't be afraid to try different types of problems. You've got this! If you have any more questions, feel free to ask. And hey, maybe try creating your own similar problem and see if you can solve it. Good luck, and keep up the great work!