Which statement is correct when comparing (5-\sqrt{11}) and ( \frac{17}{10} ) on the number line?
Answer and explanation
Correct answer: (5-\sqrt{11}<\frac{17}{10})
To compare the two numbers, estimate the square root. Since \\(\\sqrt{11}\\) is about \\(3.316\\), the first expression is approximately \\(5-3.316=1.684\\). The second expression is \\(\\frac{17}{10}=1.7\\). These estimates are close, so careful calculation is useful, but they clearly show which value is smaller.
More precisely, \\(5-\\sqrt{11}\\approx1.6834\\), while \\(\\frac{17}{10}=1.7\\). Therefore \\(5-\\sqrt{11}<\\frac{17}{10}\\). Both values are positive and near 1.7, so the statement that both are less than \\(-1\\) is impossible. Hence option A is correct. A decimal approximation is sufficient here because the two values are not equal.
Frequently asked questions
What is the correct answer to this question?
(5-\sqrt{11}<\frac{17}{10})
Why is this the correct answer?
To compare the two numbers, estimate the square root. Since \\(\\sqrt{11}\\) is about \\(3.316\\), the first expression is approximately \\(5-3.316=1.684\\). The second expression is \\(\\frac{17}{10}=1.7\\). These estimates are close, so careful calculation is useful, but they clearly show which value is smaller.
More precisely, \\(5-\\sqrt{11}\\approx1.6834\\), while \\(\\frac{17}{10}=1.7\\). Therefore \\(5-\\sqrt{11}<\\frac{17}{10}\\). Both values are positive and near 1.7, so the statement that both are less than \\(-1\\) is impossible. Hence option A is correct. A decimal approximation is sufficient here because the two values are not equal.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Representing real numbers on the number line.
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