Using rational approximations, what is an inequality statement comparing 21−−√ and 17−−√ ? Enter <, >, or =.(1 point) The inequality is: 21−−√ 17−−√ .

Answer 1

To compare \( \sqrt{21} \) and \( \sqrt{17} \), we can compare their squares instead. This is because the square function is monotonically increasing for positive numbers:

1. Calculate the squares:

   • \( \sqrt{21}^2 = 21 \)
   • \( \sqrt{17}^2 = 17 \)

2. Now compare the squared numbers:

   • Since \( 21 > 17 \), it follows that \( \sqrt{21} > \sqrt{17} \).

Thus, the inequality is:

\[ \sqrt{21} > \sqrt{17} \]

So the answer is:

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