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

Question

The inequality is: 21−−√
17−−√.

Answer 1

To compare the two expressions, we can use the properties of inequalities and irrational numbers.

Let's approximate √21 and √17 to rational numbers. We know that √16 = 4 and √25 = 5, so we can estimate that √21 is between 4 and 5.

Similarly, we know that √16 = 4 and √9 = 3, so we can estimate that √17 is between 3 and 4.

Since 4 > 3, and √21 is greater than √17, we can conclude that:

√21 > √17

Therefore, the inequality statement is:

21−−√ > 17−−√