Which inequality represents the interval of tenths that the square root of 14 lies between?

3.7 < √14 < 3.8

Step-by-step explanation:

First approximation

9 < 14 < 16, so

3 < √14 < 4

Second approximation

14 is closer to 16 than to 9.

Is √14 between 3.7 and 3.8? If so, then

3.7² < 14 < 3.8²

13.69 < 14 < 14.44. TRUE

The inequality is 3.7 < √14 < 3.8.