Which of the following is the closest approximation for the square root of 14?

To find the closest approximation for the square root of 14, it is beneficial to first identify two perfect squares that surround 14. The square root of 9 is 3, and the square root of 16 is 4. This means that the square root of 14 will fall somewhere between 3 and 4.

Next, calculating more precisely, we can see that the square root of 14 is approximately 3.74 when computed (since 3.74 squared is approximately 13.9, which is close to 14). Therefore, 3.74 is a reasonable approximation that is very close to the actual value.

Choosing options like 3.61, 3.87, or 4.00 either underestimates or overestimates the value significantly when compared to the accurate calculation of the square root of 14. Hence, the option that is closest to the square root of 14 is 3.74.