What type of number is \((-3\sqrt{11})\)?
Answer and explanation
Correct answer: Irrational
Since 11 is not a perfect square, \(\sqrt{11}\) is irrational. Multiplying an irrational number by the non-zero rational number \(-3\) gives an irrational result. Therefore, \(-3\sqrt{11}\) is irrational. It cannot be a natural number or zero because it is negative. Exam tip: The square root of a non-perfect square is irrational.
Frequently asked questions
What is the correct answer to this question?
Irrational
Why is this the correct answer?
Since 11 is not a perfect square, \(\sqrt{11}\) is irrational. Multiplying an irrational number by the non-zero rational number \(-3\) gives an irrational result. Therefore, \(-3\sqrt{11}\) is irrational. It cannot be a natural number or zero because it is negative. Exam tip: The square root of a non-perfect square is 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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