If \(x=2+\sqrt{3}\), what type of number is (x)?
Answer and explanation
Correct answer: Irrational
\(2\) is rational, while \(\sqrt{3}\) is irrational because 3 is not a perfect square. The sum of a rational number and an irrational number is always irrational. Therefore, \(x=2+\sqrt{3}\) is irrational. Integers and natural numbers are rational, so neither can be correct here. Exam tip: rational \(+\) irrational is always irrational.
Frequently asked questions
What is the correct answer to this question?
Irrational
Why is this the correct answer?
\(2\) is rational, while \(\sqrt{3}\) is irrational because 3 is not a perfect square. The sum of a rational number and an irrational number is always irrational. Therefore, \(x=2+\sqrt{3}\) is irrational. Integers and natural numbers are rational, so neither can be correct here. Exam tip: rational \(+\) irrational is always irrational.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Irrational numbers.
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