  Optical measurement of the motion of a 940 kHz mechanical resonance of a
silicon nitride nanostring resonator is demonstrated with a read out noise
imprecision reaching 37 dB below that of the resonator's zero-point
fluctuations. Via intensity modulation of the optical probe laser, radiation
pressure feedback is used to cool and damp the mechanical mode from an initial
room temperature occupancy of $\bar{n}_{b} = 6.5 \times 10^6$ ($T_{b}=295$K)
down to a phonon occupation of $\langle n \rangle = 66 \pm 10$, representing a
mode temperature of $T_{m} \approx 3$mK. The five decades of cooling is enabled
by the system's large single-photon cooperativity $(C_{1} = 4)$ and high
quantum efficiency of optical motion detection ($\eta_{t} = 0.27$).
