Math Problem Statement

Simplify or analyze the mathematical expression \( \sqrt{11 \cdot (\sqrt{7} + \sqrt{13})} \).

Solution

The mathematical expression in the image is:

11(7+13)\sqrt{11 \cdot (\sqrt{7} + \sqrt{13})}

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5 Related Questions:

  1. What are the properties of square roots when multiplied or added?
  2. Can the given expression be simplified further using factorization or approximations?
  3. How does one rationalize expressions involving square roots?
  4. What is the approximate value of this expression if calculated?
  5. How are square roots applied in real-world contexts like geometry?

Tip:

Always check if square roots in a product can be simplified by factoring out perfect squares to simplify calculations!

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Math Problem Analysis

Mathematical Concepts

Square Roots
Simplification of Radical Expressions
Basic Algebra

Formulas

\( \sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b} \)
\( \sqrt{a + b} \) cannot be split into \( \sqrt{a} + \sqrt{b} \)

Theorems

Properties of Square Roots

Suitable Grade Level

Grades 9-10