<span>A is rational</span>
<span>B is irrational</span>
<span>Product of a and b is irrational.</span>
Subtract the smaller median (30) from the larger (55). The result, 25, is the average improvement in test scores from the pretest score to the posttest score.
Let f(x) = sqrt(x). Use linear approximation about x = 25, since 24 is close to 25, and since it is easy to take the square root of 25.
Note that f ' (x) = 1/[2sqrt(x)] from the power rule.
About x = 25, f(x) is approximately f(25) + f ' (25)(x - 25).
So sqrt(24) = f(24) is approximately
f(25) + f ' (25)(24 - 25) = sqrt(25) + {1/[2sqrt(25)]}(-1) = 5 - 1/10 = 4.9 .