QQuestionMathematics
QuestionMathematics
Find the two whole numbers that are the closest to $\sqrt{42}$.
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Explain your reasoning.
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Answer
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Step 1:I'll solve this step by step using precise mathematical reasoning:
Step 2:: Understand the problem
- We need to find the two whole numbers that are closest to $$\sqrt{42}
- This means finding the integers that \sqrt{42} falls between
Step 3:: Calculate \sqrt{42}
- $$\sqrt{42} \approx 6.480740698407860
- This means \sqrt{42} is between 6 and 7
Step 4:: Verify the bounds
- This confirms that 6 and 7 are the two whole numbers closest to $$\sqrt{42}
- 7^{2} = 49 (which is greater than 42)
Step 5:: Check proximity
- Distance from 6: $$|\sqrt{42} - 6| \approx 0.480740698
- Distance from 7: |7 - \sqrt{42}| \approx 0.519259302
Final Answer
The two whole numbers closest to \sqrt{42} are 6 and 7.
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