Which of the following numbers is irrational and can be represented by a unique point on the number line?
Answer and explanation
Correct answer: \(\sqrt{2}\)
\(\sqrt{2}\) is irrational because it cannot be written as \(\frac{p}{q}\), and its decimal expansion is non-terminating and non-repeating. In contrast, 0.375 is a terminating decimal, so it is rational. Exam tip: the square root of a non-perfect square is usually irrational.
Frequently asked questions
What is the correct answer to this question?
\(\sqrt{2}\)
Why is this the correct answer?
\(\sqrt{2}\) is irrational because it cannot be written as \(\frac{p}{q}\), and its decimal expansion is non-terminating and non-repeating. In contrast, 0.375 is a terminating decimal, so it is rational. Exam tip: the square root of a non-perfect square is usually irrational.
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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