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QuestionMathematics
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Simplify $\sqrt{63}$.
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Answer
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Step 1:I'll solve this step by step, focusing on simplifying the square root of 63.
Step 2:: Identify the factors of 63
63 = 3^{2} \times 7
Step 3:: Separate the perfect square factor
- The largest perfect square factor is $$3^{2} = 9
- The remaining factor is 7
Step 4:: Rewrite the square root
\sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7}
Step 5:: Simplify
\sqrt{63} = 3 \sqrt{7}
Final Answer
The solution involves: - Breaking down 63 into its prime factors - Identifying the largest perfect square factor (9) - Separating the square root - Simplifying to 3\sqrt{7}
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