# How do you use a linear approximation to approximate the value of #root(3)(27.5)#?

Hence,

Recalll the equation of a line is given by

Hopefully this helps!

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To use linear approximation to approximate the value of (\sqrt[3]{27.5}), first, choose a function to approximate with. A common choice is the linear function (f(x) = f(a) + f'(a)(x - a)). Then, find a point (a) close to the value you want to approximate. For (\sqrt[3]{27.5}), a reasonable choice is (a = 27). Next, calculate the derivative of the function, (f'(x)), and evaluate it at (a). For (\sqrt[3]{x}), the derivative is (\frac{1}{3}x^{-2/3}). So, (f'(27) = \frac{1}{3}(27)^{-2/3}). Finally, plug (a), (f(a)), and (f'(a)) into the linear approximation formula and solve for (x). This gives the approximate value of (\sqrt[3]{27.5}).

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