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The decimal expansion of √2 is:
- a)Terminating
- b)Repeating
- c)Non-terminating and non-repeating
- d)Rational
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The decimal expansion of √2 is:a)Terminatingb)Repeatingc)Non-terminati...
Assume √2 is rational, so √2 = a/b with integers a,b in lowest terms and b ≠ 0.
Squaring gives 2 = a2/b2, hence a2 = 2b2. Thus a2 is even, so a is even; write a = 2k.
Then (2k)2 = 4k2 = 2b2, so b2 = 2k2, which implies b is even.
Both a and b being even contradicts that a/b is in lowest terms. Therefore √2 is irrational.
Therefore its decimal expansion is non-terminating and non-repeating.
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