What does assuming √3 = a/b mean?
Answer and explanation
Correct answer: Assuming it is rational
Writing √3 as a/b means assuming that √3 is rational, because a rational number is defined as a number that can be expressed as the quotient of two integers, with a non-zero denominator. In the proof, a and b are selected as coprime integers so that a/b is in lowest form. Squaring the assumed equality gives a² = 3b², and divisibility by 3 eventually forces both a and b to have a factor 3. That contradicts their coprime condition and proves that the assumption was impossible. Therefore option B is correct. Being written as a fraction does not mean the number is an integer, zero, or negative; those are different properties.
Frequently asked questions
What is the correct answer to this question?
Assuming it is rational
Why is this the correct answer?
Writing √3 as a/b means assuming that √3 is rational, because a rational number is defined as a number that can be expressed as the quotient of two integers, with a non-zero denominator. In the proof, a and b are selected as coprime integers so that a/b is in lowest form. Squaring the assumed equality gives a² = 3b², and divisibility by 3 eventually forces both a and b to have a factor 3. That contradicts their coprime condition and proves that the assumption was impossible. Therefore option B is correct. Being written as a fraction does not mean the number is an integer, zero, or negative; those are different properties.
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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