F10-High ISO and blur

I've had my first ever digicam (f10) for about 24 hours, i must have taken over 500 test pics already, still got lots to learn.

When i get it right the Pics have great quality, but that is usually on auto mode but when I switch over to a higher iso's without flash I havent been able to capture a single shot wihout blur. I am guessing that the shutter is left on longer on the higher iso (1600), but then what is the point if i cant capture without a tripod?

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