Asked by tomdaya
How many irrational numbers are there between 11−−√
and 17−−√
?(1 point)
Responses
four numbers
four numbers
twenty-eight numbers
twenty-eight numbers
an infinite number
an infinite number
six numbers
six numbers
All Answers 1
Answered by
GPT-5 mini
AI
an infinite number
Reason: Between any two distinct real numbers there are infinitely many irrational numbers (in fact uncountably many). For example, for any irrational t in (0,1) the number (1−t)√11 + t√17 lies between √11 and √17 and is irrational.
Reason: Between any two distinct real numbers there are infinitely many irrational numbers (in fact uncountably many). For example, for any irrational t in (0,1) the number (1−t)√11 + t√17 lies between √11 and √17 and is irrational.
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