Simplifying a Complex Expression: 1/2 √3 × 1/2 √3
In mathematics, simplifying complex expressions is an essential skill to master. In this article, we will explore the process of simplifying the expression 1/2 √3 × 1/2 √3.
Understanding the Expression
The given expression is a product of two square roots of 3, each multiplied by a fraction of 1/2.
Step-by-Step Simplification
To simplify the expression, we need to follow the order of operations (PEMDAS):
- Multiply the fractions: 1/2 × 1/2 = 1/4
- Multiply the square roots: √3 × √3 = 3 (since (√3)² = 3)
- Multiply the results: 1/4 × 3 = 3/4
Final Answer
The simplified expression is 3/4.
Conclusion
In this article, we have successfully simplified the complex expression 1/2 √3 × 1/2 √3. By following the order of operations and multiplying the fractions and square roots, we arrived at the simplified answer of 3/4. This exercise demonstrates the importance of understanding the order of operations and the properties of square roots in algebra.
