To solve the expression [tex]\(3 + \sqrt{23}\)[/tex], we need to break it down into its components and follow a clear, step-by-step approach:
1. Identify the Terms:
- The first term is a constant: [tex]\(3\)[/tex].
- The second term is the square root of [tex]\(23\)[/tex], written as [tex]\(\sqrt{23}\)[/tex].
2. Calculate the Square Root:
- The square root of [tex]\(23\)[/tex] is an irrational number, so it will not be a simple integer or fraction. However, its approximate value is [tex]\(4.795831523312719\)[/tex].
3. Sum the Terms:
- Now, we simply add the two terms together:
[tex]\[
3 + 4.795831523312719
\][/tex]
4. Perform the Addition:
- Adding these numbers gives us:
[tex]\[
3 + 4.795831523312719 = 7.795831523312719
\][/tex]
Therefore, the value of the expression [tex]\(3 + \sqrt{23}\)[/tex] is approximately [tex]\(7.795831523312719\)[/tex].
