Math Problem Statement

Simplify the expression \( \sqrt{8} + 3\sqrt{2} \).

Solution

The expression in the image is:

8+32\sqrt{8} + 3\sqrt{2}

Step-by-step simplification:

  1. Simplify 8\sqrt{8}: 8=4×2=4×2=22\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}

  2. Now substitute 8\sqrt{8} with 222\sqrt{2}: 22+322\sqrt{2} + 3\sqrt{2}

  3. Combine like terms (both terms contain 2\sqrt{2}): (2+3)2=52(2 + 3)\sqrt{2} = 5\sqrt{2}

Thus, the simplified form of the expression is:

525\sqrt{2}

Let me know if you'd like more details or further clarification!

Related Questions:

  1. How do you simplify other square roots like 18\sqrt{18}?
  2. Can you explain how to factor numbers inside square roots?
  3. What are like terms in radical expressions, and how do you combine them?
  4. How do you simplify 12+27\sqrt{12} + \sqrt{27}?
  5. Can you solve expressions involving cube roots?

Tip:

Always look for perfect square factors within a square root to simplify expressions more easily.

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Math Problem Analysis

Mathematical Concepts

Radicals
Simplifying Expressions

Formulas

\( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \)
Combining like terms

Theorems

Properties of Radicals

Suitable Grade Level

Grades 8-10