Sure, let's break down the expression [tex]\(4 \sqrt{3} - 3 \sqrt{5}\)[/tex] step-by-step to understand its value.
1. Identify the Components:
- The expression consists of two terms: [tex]\(4 \sqrt{3}\)[/tex] and [tex]\(-3 \sqrt{5}\)[/tex].
2. Evaluate Each Part:
- [tex]\(\sqrt{3}\)[/tex] is an irrational number approximately equal to 1.732.
- [tex]\(\sqrt{5}\)[/tex] is an irrational number approximately equal to 2.236.
3. Multiply by Constants:
- Multiply [tex]\(4 \sqrt{3}\)[/tex] to get approximately [tex]\(4 \times 1.732 = 6.928\)[/tex].
- Multiply [tex]\(-3 \sqrt{5}\)[/tex] to get approximately [tex]\(-3 \times 2.236 = -6.708\)[/tex].
4. Combine the Results:
- Add the results of the two parts: [tex]\(6.928 - 6.708 = 0.22\)[/tex].
Therefore, the value of the expression [tex]\(4 \sqrt{3} - 3 \sqrt{5}\)[/tex] is approximately [tex]\(0.22\)[/tex].
