Answer
$\dfrac{99}{8}$
Work Step by Step
The formula to calculate the arc length is as follows:
$L=\int_m^n \sqrt {1+[f'(x)]^2} dx$
Re-write the equation as follows:
$[f'(x)]^2=\dfrac{(y-1)^2}{4y}$
This implies that
$L=\int_{1}^{8} [1+\dfrac{(4x^{2/3}-1)^2}{16x^{2/3}}] dx $
Separate the terms and integrate as follows:
$L=\int_{1}^{8} \dfrac{4x^{2/3}+1}{4x^{1/3}} dy \\=[ \dfrac{3x^{4/3}}{4}-\dfrac{3x^{2/3}}{8} ]_1^{8}=\dfrac{99}{8}$
