Question

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

Answer 1

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.