If the gamma-ray burst sources detected by GRO are coalescing binaries at cosmological distances there should be a coincident gravitational radiation signal. Using the GRBs rate we predict the gravitational radiation detection rate as a function of the gravitational wave strain at Earth. This method of predicting the rate avoids the large statistical uncertainties in the current estimates that are based on the three neutron star binaries containing pulsars found, so far, in the Galaxy. The brightest gamma-ray bursts should be accompanied by a gravitational pulse detectable by LIGO or VIRGO, and by using the bursts as triggers for LIGO/VIRGO their sensitivity can be improved by 50% and the detection rate increases by a factor of 3. LIGO/VIRGO must reach a strain sensitivity of 10(-20.7) h0 to detect one burst per decade, and a failure to find coincidences at a rate of one per year with a strain sensitivity of 10(-21.6) h0 will rule out the binary hypothesis. If they are detected as gravitational wave sources, the time delay between the gamma-rays and the gravitational waves will help to determine the burst mechanism, and the polarization of the gravitational waves will help to determine the burst geometry.