Between which pair of rational numbers on a number line does sqrt(38) lie?
A. between 6.3 and 6.5
B. Between 19 and 19.2
C. Between 18.9 and 19.1
D. Between 6.1 and 6.2
To determine the approximate location of √38 on the number line, it is first helpful to find the perfect squares that fall closest to 38. The perfect squares of 36 and 49 are the closest to 38 since 6^2=36 and 7^2=49. Since 38 is closer to 36, we can conclude that √38 is between √36 and √49, which is between 6 and 7.
Among the given answer choices, √38 lies between 6.1 and 6.2. Therefore, the correct answer is option (D) Between 6.1 and 6.2.