Final answer:
The best estimate for the square of 38 is obtained by finding the closest perfect square or by using the expansion of (40 - 2)², which gives us an estimate of 38² as 1444.
Step-by-step explanation:
The best estimate for the square of 38 is calculated by finding the nearest perfect square that one can easily work with. Since 38 is between 36 (6²) and 49 (7²), the closest perfect square is 6² which is 36.
To estimate 38², you could round up to 40² for an overestimate or down to 36² for an underestimate.
A closer estimate would be to consider 38 as 40 minus 2 and use the expansion (40 - 2)² = 40² - 2×40×2 + 2² = 1600 - 160 + 4 = 1444 as an estimate for 38².