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QuestionMathematics

Simplify: √224
12 months agoReport content

Answer

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Step 1:
I'll solve this step by step using the specified LaTeX formatting guidelines:

Step 2:
: Identify the number under the square root

\sqrt{224}

Step 3:
: Find the largest perfect square factor of 224

• $$224 = 2^{5} \times 7
• First, let's break down 224 into its prime factorization

Step 4:
: Separate the perfect square factor

• $$\sqrt{224} = \sqrt{2^{4} \times 2 \times 7}
\sqrt{224} = \sqrt{16 \times 2 \times 7}

Step 5:
: Simplify the square root

• $$\sqrt{224} = \sqrt{16} \times \sqrt{2 \times 7}
\sqrt{224} = 4 \times \sqrt{14}

Final Answer

Key insights: - Always look for the largest perfect square factor - Separate the square root into a coefficient and remaining radical - Simplify when possible