Using rational approximations, what is an inequality statement comparing 21−−√ and 17−−√? Enter <, >, or =.(1 point)
To compare the values of 21−−√ and 17−−√ using rational approximations, we can use the fact that √21 is approximately 4.58 and √17 is approximately 4.12. Hence, we have:
√21 ≈ 4.58
√17 ≈ 4.12
Since 4.58 > 4.12, we can conclude that:
21−−√ > 17−−√
To compare the values of √21 and √17 using rational approximations, we need to find values that are close to their actual values.
The square root of 21 is approximately 4.5826 and the square root of 17 is approximately 4.1231.
Comparing these values, we can see that √21 is greater than √17.
Therefore, the inequality statement comparing the two is: √21 > √17.
To compare the values of 21√ and 17√ using rational approximations, we can start by finding the decimal approximations for both numbers.
To do this, we can use a calculator or a mathematical software. The decimal approximation for 21√ is approximately 4.58258, and the decimal approximation for 17√ is approximately 4.12311.
Now, we can compare the decimal approximations:
4.58258 > 4.12311
Therefore, we can conclude that 21√ is greater than 17√.
The inequality statement comparing 21√ and 17√ is:
21√ > 17√