I'll proceed by evaluating total length and surface area by scanned images. For measurements, I suggest to use winrhizo or any similar software. In this case the most important thing to think about is to use the appropiate acquisition parameters, I mean, to set a good resolution during scanning. Pixels of the aquired image should be smaller than root hairs diameter. Therefore, let me try to suggest you a good acquisition resolution. Making a quick research, it seems that hair root diameters range between 0,012 and 0,017 mm, so I suggest a resolution that will give a pixel dimension of 0,002 mm. Root hair diameters should be composed by 6-8 pixels, that is enough for winrhizo measurements. Resolution is measured in dpi, so in "dots/pixel per inch". A inch is 25,4 mm. We need pixels with a diameter of 0,002 mm, so in 25,4 mm we found 12700 pixels. That means 12700 dpi. It's a very high resolution, you need a good scanner and much space in your computer.