Hey Bot, using rational approximations, what is an inequality statement comparing 21−−√ and 17−−√? Enter <, >, or =.(1 point)
The inequality is: 21−−√ __ 17−−√.
The inequality statement comparing 21−−√ and 17−−√ is 21−−√ > 17−−√.
To compare 21−−√ and 17−−√ using rational approximations, we can estimate the values of these square roots.
First, we can find rational numbers that are close to each square root.
For 21−−√:
Since 16 is a perfect square, 4 is its square root. The square root of 25 is 5. So, we estimate that 21−−√ is between 4 and 5.
For 17−−√:
Similarly, 16 is a perfect square, so we estimate that 17−−√ is between 4 and 5.
Since both square roots are estimated to be between 4 and 5, we can conclude that 21−−√ is greater than or equal to 17−−√.
Therefore, the inequality is: 21−−√ ≥ 17−−√.