Which value is greater than \(\frac{23}{6}\) and less than \(\sqrt{15}\)?
Answer and explanation
Correct answer: 3.86
The governing idea is comparison of a rational number, an irrational number, and decimal candidates. First, 23/6 = 3.833333... . Also, since 3.87² = 14.9769 and 3.88² = 15.0544, √15 is approximately 3.873. Thus the required interval is approximately 3.833 < x < 3.873. Option C, 3.86, lies inside this interval. Option A, 3.82, is too small; options B and D, 3.90 and 4.00, are greater than √15. Therefore only option C satisfies both strict inequalities. The endpoints themselves would not be accepted even if listed, because the wording says greater than and less than.
Frequently asked questions
What is the correct answer to this question?
3.86
Why is this the correct answer?
The governing idea is comparison of a rational number, an irrational number, and decimal candidates. First, 23/6 = 3.833333... . Also, since 3.87² = 14.9769 and 3.88² = 15.0544, √15 is approximately 3.873. Thus the required interval is approximately 3.833 < x < 3.873. Option C, 3.86, lies inside this interval. Option A, 3.82, is too small; options B and D, 3.90 and 4.00, are greater than √15. Therefore only option C satisfies both strict inequalities. The endpoints themselves would not be accepted even if listed, because the wording says greater than and less than.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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