Concept: Let small change in x be ?x and the corresponding change in y is ?y.Therefore \(\rm ? y = \rm \frac{dy}{dx}? x\)Calculation:We have to find the value of \(\rm (17)^{1/4}\)Let x + ?x = 17 = 16 + 1Therefore, x = 16 and ?x = 1Assume, \(\rm y = x^{1/4}\) Differentiating with respect to x, we get\(\rm \Rightarrow \frac{dy}{dx} = \frac{1}{4}x^{-3/4} = \frac{1}{4(x)^{3/4}}\)At x = 16\(\rm \left[\frac{dy}{dx} \right ]_{x=16} = \frac{1}{32}\) and y = \(\rm (16)^{1/4} = 2\)As we know \(\rm ? y = \rm \frac{dy}{dx}? x\)So, \(\rm ? y = \frac{1}{32} \times 1 = 0.03125\)Therefore, approximate value of \(\rm (17)^{1/4}\) = y + ?y = 2 + 0.03125 = 2.03125