Question

why does clear sky look blue

Answer 1

because blue scatter the most through tiny atmospheric particles

Answer 2

The scattering of blue component of the white light by air molecules present in the atmosphere causes the blue colour of the sky.
when sunlight passes through the atmosphere, the molecules in air like nitrogen and oxygen scatter blue part whereas most of the longer wavelength light pass straight through .whichever direction we look the scattered blue light enters our eye.