Simplifying Complex Radicals: An SEO Guide to Simplifying 6sqrt{80}-4sqrt{45}
As an SEO expert, understanding how to break down complex mathematical expressions and present them in a clear, understandable format is crucial. This article will guide you through the simplification process of 6sqrt{80} - 4sqrt{45}, helping you achieve the most straightforward and SEO-friendly representation of the expression.
Understanding the Problem
The given expression, 6sqrt{80} - 4sqrt{45}, is a good example of how to apply basic algebraic principles to simplify seemingly complex algebraic expressions involving radicals. When faced with such expressions, the first step is to identify and consider the properties of the radicals (square roots, cube roots, etc.).
Breaking Down the Expression
Let's start by breaking down each term in the expression.
Term 1: 6sqrt{80}
First, simplify the square root of 80. Recognize that 80 can be broken down into its prime factors: 80 16 * 5, and further 16 4^2. Thus, we have:
6 * sqrt{80} 6 * sqrt{16 * 5} 6 * sqrt{16} * sqrt{5} 6 * 4 * sqrt{5} 24sqrt{5}
Term 2: 4sqrt{45}
Similarly, simplify the square root of 45. The prime factorization of 45 is 9 * 5, and further 9 3^2. Therefore:
4 * sqrt{45} 4 * sqrt{9 * 5} 4 * sqrt{9} * sqrt{5} 4 * 3 * sqrt{5} 12sqrt{5}
Subtracting the Terms
Now, subtract the second term from the first term:
[ 24sqrt{5} - 12sqrt{5} (24 - 12)sqrt{5} 12sqrt{5} ]The expression is now simplified to a single term, 12sqrt{5}.
Why This Matters for SEO
When working with algebraic expressions in web content, especially for educational or tutorial purposes, it is essential to present the simplified form clearly and concisely. This not only aids in user understanding but also improves the SEO of your content.
Keyword Optimization
To optimize your content for search engines, use the following keywords:
radical simplification square roots algebraic expressionsEnsure that these keywords are naturally integrated into your headings, subheadings, and throughout the content to enhance both the readability and searchability of the article.
Conclusion
In conclusion, the expression 6sqrt{80} - 4sqrt{45} simplifies to 12sqrt{5}. By breaking down the problem into its fundamental components and applying basic algebraic principles, you can achieve a clear and concise solution. This method not only aids in solving similar problems but also enhances the SEO of your content through effective keyword usage.
Frequently Asked Questions
Q: How do I simplify 6sqrt{80} - 4sqrt{45}?
A: Start by simplifying each term separately: 6sqrt{80} 24sqrt{5} and 4sqrt{45} 12sqrt{5}. Subtract the second term from the first: 24sqrt{5} - 12sqrt{5} 12sqrt{5}.
Q: Which keywords should I use for SEO optimization?
A: Use keywords such as 'radical simplification', 'square roots', and 'algebraic expressions' to enhance the SEO of your content.
Q: How does keyword optimization help with SEO?
A: Keyword optimization helps in improving the visibility and relevance of your content to search engines, making it easier for users to find your content through search queries related to your topic.