Which statement about √3 is correct?
Answer and explanation
Correct answer: √3 is irrational
The correct statement is that √3 is irrational. If √3 were rational, write it as a/b in lowest form, where a and b are coprime integers and b is non-zero. Squaring gives a² = 3b². Hence 3 divides a², so 3 divides a; write a = 3k. Substitution then gives b² = 3k², so 3 divides b as well. This contradicts the assumption that a and b are coprime. Therefore √3 cannot be expressed as a ratio of integers and is irrational, making option B correct. It is not an integer or a natural number because its square is 3, which is not the square of an integer; it is also clearly not zero because 0² is 0.
Frequently asked questions
What is the correct answer to this question?
√3 is irrational
Why is this the correct answer?
The correct statement is that √3 is irrational. If √3 were rational, write it as a/b in lowest form, where a and b are coprime integers and b is non-zero. Squaring gives a² = 3b². Hence 3 divides a², so 3 divides a; write a = 3k. Substitution then gives b² = 3k², so 3 divides b as well. This contradicts the assumption that a and b are coprime. Therefore √3 cannot be expressed as a ratio of integers and is irrational, making option B correct. It is not an integer or a natural number because its square is 3, which is not the square of an integer; it is also clearly not zero because 0² is 0.
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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