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A series of storms drenching the eastern part of the state has dropped water that has yet to crest, leaving damage that could take years to repair, said Beshear, who declared a state of emergency in six counties on Thursday morning (local time).
"We are currently experiencing one of the worst, most devastating flooding events in Kentucky's history, Beshear said in his emergency declaration.
"Hundreds will lose their homes."
Among the dead was an 81-year-old woman in the Perry County.
"This is an ongoing natural disaster, with more rain expected tonight that could worsen the situation," the governor said on Twitter.
The flooding left 23,000 households without power, and "a number of people" were unaccounted for, he said.
Roads looked like rivers, with water as high as the leaves of nearby trees and power poles sticking up from greenish brown water, in videos posted by local media.
The state activated the national guard and the state police to use helicopters and boats to rescue people marooned among the floodwaters, Beshear said.
Evacuation centers were opened in state parks and other facilities, but Beshear warned that some of the facilities themselves were hard-hit by the storms, and may not have power or some amenities.
Fresh water will also be difficult to find in parts of the flooded region, and so trucks will be bringing in drinking water, he said.
There was a 40 percent chance that the hard-hit area around the city of Hazard in the Cumberland Mountain foothills in Appalachia would continue to see heavy rain and storms through the night on Thursday, and an 80% chance on Friday, the National Weather Service said.
The region remains under a flood warning.