Simplifying 1/2 + 1/2√2
In mathematics, simplifying expressions is an essential skill to master. One such expression that may seem daunting at first is 1/2 + 1/2√2. In this article, we will break down this expression and simplify it to its most basic form.
What is √2?
Before we dive into simplifying the expression, let's take a quick look at what √2 is. The square root of 2, denoted by √2, is an irrational number that represents the positive square root of the number 2. It is an essential constant in mathematics and appears in many mathematical formulas, including geometry, algebra, and calculus.
Simplifying 1/2 + 1/2√2
Now, let's get back to our original expression: 1/2 + 1/2√2. At first glance, it may seem like a complicated expression, but fear not! We can simplify it using some basic algebraic properties.
Step 1: Combine like terms
The first step is to combine the two terms with the same denominator, which is 2. We can rewrite the expression as:
1/2 + 1/2√2 = (1 + √2)/2
Simplified Expression
And there you have it! The simplified expression is:
(1 + √2)/2
This expression is now in its simplest form, and we can use it for further calculations or manipulations.
Conclusion
Simplifying expressions like 1/2 + 1/2√2 may seem intimidating at first, but by breaking it down step by step, we can arrive at a simplified form. Remember to combine like terms and use basic algebraic properties to simplify expressions. With practice, you'll become proficient in simplifying even the most complex expressions!
