If x = √6, what type of number is 2x?
Answer and explanation
Correct answer: Irrational number
The governing concept is the closure property of rational multiplication with an irrational number. Substituting x = √6 gives 2x = 2√6. The number √6 is irrational because 6 is not a perfect square, so its decimal expansion is non-terminating and non-repeating. Multiplying an irrational number by a non-zero rational number such as 2 cannot make it rational: if 2√6 were rational, dividing it by 2 would make √6 rational, which is a contradiction. Therefore option C is correct. It is not an integer, rational number, or zero; the coefficient 2 only changes its magnitude.
Frequently asked questions
What is the correct answer to this question?
Irrational number
Why is this the correct answer?
The governing concept is the closure property of rational multiplication with an irrational number. Substituting x = √6 gives 2x = 2√6. The number √6 is irrational because 6 is not a perfect square, so its decimal expansion is non-terminating and non-repeating. Multiplying an irrational number by a non-zero rational number such as 2 cannot make it rational: if 2√6 were rational, dividing it by 2 would make √6 rational, which is a contradiction. Therefore option C is correct. It is not an integer, rational number, or zero; the coefficient 2 only changes its magnitude.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Irrational numbers.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
