Which of the following statements is correct about representing the irrational number \(\sqrt{2}\) on the number line?
Answer and explanation
Correct answer: Even though its decimal expansion is non-terminating and non-repeating, it can be represented by a definite point on the number line.
\(\sqrt{2}\) is irrational, but every real number has a unique point on the number line. Since \(1^2<2<2^2\), it lies between 1 and 2. Option B wrongly treats a non-terminating decimal as unrepresentable; use consecutive squares in exams.
Frequently asked questions
What is the correct answer to this question?
Even though its decimal expansion is non-terminating and non-repeating, it can be represented by a definite point on the number line.
Why is this the correct answer?
\(\sqrt{2}\) is irrational, but every real number has a unique point on the number line. Since \(1^2<2<2^2\), it lies between 1 and 2. Option B wrongly treats a non-terminating decimal as unrepresentable; use consecutive squares in exams.
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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