2.jpeg "(1/2√3)2")
Simplifying the Expression: (1/2√3)²
In this article, we will explore the simplification of the algebraic expression (1/2√3)². This expression involves a fraction, a square root, and an exponent, making it an interesting mathematical topic to dive into.
Breaking Down the Expression
Let's break down the given expression into its constituent parts:
1/2 is a fraction, √3 is a square root, and ² is an exponent indicating "squared". To simplify this expression, we need to follow the order of operations (PEMDAS) and evaluate the expression from inside out.
Evaluating the Square Root
First, let's focus on the square root part: √3. The square root of 3 is an irrational number, approximately equal to 1.732. We can rewrite the expression as:
(1/2 × 1.732)²
Simplifying the Fraction
Next, let's simplify the fraction part: 1/2 × 1.732. Using multiplication, we get:
0.866
Applying the Exponent
Now, we're left with 0.866². To evaluate this, we need to square 0.866, which gives us:
0.75
Final Answer
Thus, the simplified expression (1/2√3)² equals 0.75. This result demonstrates how to simplify an algebraic expression involving fractions, square roots, and exponents.
Conclusion
In conclusion, by breaking down the expression (1/2√3)² and following the order of operations, we successfully simplified it to its final form, 0.75. This exercise showcases the importance of understanding fractions, square roots, and exponents in algebraic expressions.
