Let's evaluate each of your statements one by one:
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Irrational number between 9 and 11: \( \sqrt{99} \)
This is correct. Since \( \sqrt{99} \) is approximately 9.95, it lies between 9 and 11, and it is an irrational number. -
Least integer whose square root is an irrational number between 5 and 7: 26
This is correct. The square root of 26 is approximately 5.1, which is between 5 and 7, and \( \sqrt{26} \) is irrational. -
Rational number that is between \( \sqrt{10} \) and \( \sqrt{11} \): \( \frac{16}{5} \) (or 3.2)
This is correct. \( \sqrt{10} \) is about 3.162 and \( \sqrt{11} \) is about 3.317, and \( \frac{16}{5} = 3.2 \), which lies between them. -
Irrational number that is between \( \sqrt{14} \) and \( \sqrt{18} \): \( \sqrt{15} \)
This is correct. Since \( \sqrt{14} \) is approximately 3.74 and \( \sqrt{18} \) is approximately 4.24, \( \sqrt{15} \) (approximately 3.87) is indeed between them and is irrational. -
How many irrational numbers are there between \( \sqrt{11} \) and \( \sqrt{17} \)? An infinite number
This is correct. There are indeed infinitely many irrational numbers in any interval of real numbers, including between \( \sqrt{11} \) (approximately 3.317) and \( \sqrt{17} \) (approximately 4.123).
In summary, all of your statements are correct. Well done!
3 answers