Answer
OQ=7.84
Work Step by Step
Name the point where AB and OQ intersect point M.
OM$^2$=AO$^2$-AM$^2$
OM$^2$=16-9=7
OM=$\sqrt 7$$\approx$2.64
QM$^2$=AQ$^2$-AM$^2$
QM$^2$=36-9=27
QM=3$\sqrt 3$$\approx$5.2
OQ=OM+MQ
OQ=2.64+5.2
OQ=7.84