Math Problem Statement

Give me 3 more problems to solve!

Give me 3 more problems to solve!

Solution

The given problem is:

862248\sqrt{6} - 2\sqrt{24}

Solution:

  1. Simplify 24\sqrt{24}:
    24=46=26\sqrt{24} = \sqrt{4 \cdot 6} = 2\sqrt{6}

  2. Substitute 24\sqrt{24} in the expression:
    862(26)=86468\sqrt{6} - 2(2\sqrt{6}) = 8\sqrt{6} - 4\sqrt{6}

  3. Combine like terms:
    (84)6=46(8 - 4)\sqrt{6} = 4\sqrt{6}

Final Answer:

464\sqrt{6}


3 Problems for You to Solve:

  1. Simplify:
    58+3505\sqrt{8} + 3\sqrt{50}

  2. Simplify:
    71848+2727\sqrt{18} - 4\sqrt{8} + 2\sqrt{72}

  3. Simplify:
    1045320+510\sqrt{45} - 3\sqrt{20} + \sqrt{5}


Tip:

When simplifying square roots, always factorize the number inside the root to find perfect squares (e.g., 24=46\sqrt{24} = \sqrt{4 \cdot 6}) for easier reduction.

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Math Problem Analysis

Mathematical Concepts

Simplifying Square Roots
Algebraic Expressions

Formulas

\( \sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b} \)
Combine like terms in expressions

Theorems

Properties of Square Roots

Suitable Grade Level

Grades 6-9