Math Problem Statement

Simplify the expression: \(\frac{2(2 + 7) - 6(3)}{\sqrt{2} + 5}\).

Solution

The image contains a mathematical expression that seems to involve simplifying or evaluating an algebraic expression. From what I can extract, the key expression appears to be:

2(2+7)6(3)2+5\frac{2(2 + 7) - 6(3)}{\sqrt{2} + 5}

This expression was then simplified or evaluated, and the work seems to be double-checked, leading to the final answer 2\boxed{2}.

Would you like a detailed step-by-step explanation of how to simplify or evaluate this expression? If so, I can provide that, or if there's something specific you'd like to focus on, just let me know.


Further Questions for Exploration:

  1. How do you simplify an expression with both radicals and integers in the denominator?
  2. What are the properties of square roots that help in simplifying expressions like these?
  3. How can you check your work when simplifying complex expressions?
  4. What role do parentheses play in evaluating algebraic expressions correctly?
  5. How do the order of operations affect the outcome of an algebraic expression?

Tip: Always ensure to follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) when simplifying any algebraic expression.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplification
Radicals
Order of Operations

Formulas

Order of Operations (PEMDAS)
Basic Properties of Square Roots

Theorems

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Suitable Grade Level

Grades 8-10