Check out somthing called "project orion", they did seriously think about this and built small scale test models that worked.
A Quote :-
"Orion is one of the great "what if's" of the twentieth century. Today, nuclear powered spaceships seem like little more than laughably naive
1950's science fiction, but it might have been otherwise...and still could be. Orion was a project aimed at discovering the feasibility of spaceships
driven by nuclear bombs.
The initial plan called for manned missions to Mars by 1965 and Saturn by 1970. After seven years of work, the project's technical challenges seemed
surmountable, but political obstacles brought the effort to a halt"
"A project to explore the feasibility of building a nuclear-pulse rocket powered by nuclear fission. It was carried out by physicist Theodore Taylor
and others over a seven-year period, beginning in 1958, with United States Air Force support. The propulsion system advocated for the Orion spacecraft
was based on an idea first put forward by Stanislaw Ulam and Cornelius Everett in a classified paper in 1955. Ulam and Everett suggested releasing
atomic bombs behind a spacecraft, followed by disks made of solid propellant. The bombs would explode, vaporizing the material of the disks and
converting it into hot plasma. As this plasma rushed out in all directions, some of it would catch up with the spacecraft, impinge upon a pusher
plate, and so drive the vehicle forward.
Project Orion originated at General Atomics in San Diego, a company (later a subsidiary of General Dynamics) founded by Frederick de Hoffman to
develop commercial nuclear reactors. It was de Hoffman who persuaded Freeman Dyson to join Taylor in San Diego to work on Orion during the 1958-59
Ulam and Everett's idea was modified so that instead of propellant disks, the propellant and bomb were combined into a single pulse unit. Plastic was
chosen as the propellant material, not only because of its effectiveness in absorbing the neutrons emitted by an atomic explosion but also because it
breaks down into lightweight atoms such as those of hydrogen and carbon which move at high speed when hot. This approach, in tandem with the pusher
plate concept, offered a unique propulsion system that could simultaneously produce high thrust with high exhaust velocity. The effective specific
impulse could theoretically be as high as 10,000 to one million seconds. A series of abrupt jolts would be experienced by the pusher plate, so
powerful that, if these forces were not spread out in time, they would result in acceleration surges that were intolerable for a manned vehicle.
Consequently, a shock absorbing system was devised so that the impulse energy delivered to the plate could be stored and then gradually released to
the vehicle as a whole.
Various mission profiles were considered, including an ambitious interstellar version. This called for a 40-million-ton spacecraft to be powered by
the sequential release of ten million bombs, each designed to explode roughly 60 m to the vehicle's rear. In the more immediate future, Orion was
envisaged as a means of transporting large expeditions to the Moon, Mars, and Saturn"