How to sort results by distance with google places api using textsearch

Yes, you cannot use radius and rankBy in same request. But you can use rankBy=distance and then count distance youself based on geometry.location.lat and geometry.location.lng. For exmaple in groovy i've done like that:

GeoPosition and Placeclasses are implemented by me, so don't expect to find them at the core libs :)

TreeMap<Double, Place> nearbyPlaces = new TreeMap<Double, Place>()

 if(isStatusOk(nearbySearchResponse))
                    nearbySearchResponse.results.each {

                def location = it.geometry.location
                String placeid = it.place_id
                GeoPosition position = new GeoPosition(latitude: location.lat,
                        longitude: location.lng)

                Place place =  new Place(position)

                double distance = distanceTo(place)
//If the place is actually in your radius (because Places API oftenly returns places far beyond your radius) then you add it to the TreeMap with distance to it as a key, and it will automatically sort it for you.

                if((distance <= placeSearcher.Radius()))
                    nearbyPlaces.put(distance, place)

            }

where distance is counted like that (Haversine formula):

public double distanceTo(GeoPosition anotherPos){

    int EARTH_RADIUS_KM = 6371;
    double lat1Rad = Math.toRadians(this.latitude);
    double lat2Rad = Math.toRadians(anotherPos.latitude);
    double deltaLonRad = Math.toRadians(anotherPos.longitude - this.longitude);

    return 1000*Math.acos(
                        Math.sin(lat1Rad) * Math.sin(lat2Rad) +
                        Math.cos(lat1Rad) * Math.cos(lat2Rad) * Math.cos(deltaLonRad)
                    ) * EARTH_RADIUS_KM;
}

Simply put nearby places allows you to search more vaguely but only return specific results. In Text Search, if you search for "restaurants", it will search for locations, establishments or names with the text "restaurants".Anything that is related to restaurants. Meanwhile in nearby search, if you search for "restaurants", it will return restaurant establishments with or without the text "restaurants" but only establishments of "restaurants"