When irrationality of \(\sqrt{3}\) is proved, which conclusion is correct?
Answer and explanation
Correct answer: \(\sqrt{3}\) is not rational
An irrational number cannot be written in the form \(p/q\), where \(p\) and \(q\) are integers and \(q\ne0\). Hence, proving that \(\sqrt{3}\) is irrational directly means that \(\sqrt{3}\) is not rational. It is neither an integer nor zero nor negative; in fact, \(\sqrt{3}>0\). Exam tip: remember that “irrational” means “not rational.”
Frequently asked questions
What is the correct answer to this question?
\(\sqrt{3}\) is not rational
Why is this the correct answer?
An irrational number cannot be written in the form \(p/q\), where \(p\) and \(q\) are integers and \(q\ne0\). Hence, proving that \(\sqrt{3}\) is irrational directly means that \(\sqrt{3}\) is not rational. It is neither an integer nor zero nor negative; in fact, \(\sqrt{3}>0\). Exam tip: remember that “irrational” means “not rational.”
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Proof of irrationality of square root 2 and square root 3.
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