Simplifying the Expression: 1/2√3 + 1
In this article, we will explore the simplification of the mathematical expression 1/2√3 + 1. This expression involves the combination of a fraction, a square root, and an integer, making it an interesting and challenging problem to simplify.
Understanding the Expression
Before we dive into the simplification process, let's break down the expression and understand each component:
- 1/2: This is a fraction, where 1 is the numerator and 2 is the denominator.
- √3: This is a square root of 3, which is an irrational number.
- + 1: This is an integer added to the previous expression.
Simplification Steps
To simplify the expression, we can start by combining the fraction and the square root:
Step 1: Combine the Fraction and the Square Root
1/2√3 = √3/2
Now, we have a single fraction with the square root in the numerator.
Step 2: Add 1 to the Expression
√3/2 + 1
To add 1 to the expression, we need to have a common denominator. In this case, we can multiply the integer 1 by the fraction 2/2 to get:
2/2 + √3/2
Step 3: Combine the Fractions
(2 + √3)/2
Simplified Expression
After simplifying the expression, we get:
(2 + √3)/2
This is the final simplified form of the original expression 1/2√3 + 1.
Conclusion
In this article, we have successfully simplified the expression 1/2√3 + 1 by combining the fraction and the square root, and then adding 1 to the expression. The final simplified form of the expression is (2 + √3)/2.
