Which option correctly gives the two nearest integers between which \(\sqrt{7}\) lies?
Answer and explanation
Correct answer: 2, 3
Since \(2^2=4\) and \(3^2=9\), we have \(4<7<9\). Hence \(2<\sqrt{7}<3\), so \(\sqrt{7}\) lies between the integers 2 and 3. The closest distractor C (3, 4) is wrong because \(\sqrt{7}\) is less than 3; B and D are evidently incorrect. Exam tip: compare the given number with consecutive perfect squares to find the integer bounds for its square root quickly.
Frequently asked questions
What is the correct answer to this question?
2, 3
Why is this the correct answer?
Since \(2^2=4\) and \(3^2=9\), we have \(4<7<9\). Hence \(2<\sqrt{7}<3\), so \(\sqrt{7}\) lies between the integers 2 and 3. The closest distractor C (3, 4) is wrong because \(\sqrt{7}\) is less than 3; B and D are evidently incorrect. Exam tip: compare the given number with consecutive perfect squares to find the integer bounds for its square root quickly.
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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