Math Problem Statement

7\sqrt{2\text{ }} $$$$ +4\sqrt2 $$$$ -\sqrt2

Solution

To simplify the given expression:

72+4227\sqrt{2} + 4\sqrt{2} - \sqrt{2}

Combine like terms:

Since all terms involve 2\sqrt{2}, we can add or subtract the coefficients:

(7+41)2=102(7 + 4 - 1)\sqrt{2} = 10\sqrt{2}

Final Answer:

10210\sqrt{2}

Would you like a detailed breakdown of this process or any additional explanations?

Related Questions:

  1. What are like terms in radical expressions, and how do we combine them?
  2. How do you simplify expressions involving different radicals?
  3. Can you expand a+b\sqrt{a} + \sqrt{b} if aba \neq b?
  4. How do you rationalize a denominator with 2\sqrt{2} in the denominator?
  5. What are the real-world applications of radical expressions?

Tip: Always ensure the radicals you're combining have the same index and radicand!

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Math Problem Analysis

Mathematical Concepts

Simplification of Radical Expressions
Addition and Subtraction of Like Terms

Formulas

Combining like terms: (a + b + c)√x = (a + b + c)√x

Theorems

Properties of Radicals: Radicals with the same radicand can be combined

Suitable Grade Level

Grades 6-8