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Can you move mount Everest with a nuke?
No. It's too heavy, and its height is just 8 km
Can you split mount Everest in pieces with a nuke in a 4000m deep hole from its spike?
According to underground nuclear explosion tests, No. You will just cause an earthquake but the mountain will still there
Solar sails, used on an asteroid's apoaxis, can change its orbit radically.
Nukes uses all their energy in a very short time in 360 degrees.
Most of their energy gets lost to the 180 degree side away from the asteroid. The most of the rest of the energy would become heat, and should just warm up the asteroid surface for a couple of Celsius degrees.
To move the asteroid, or to make it blow up, kinetic energy is needed.
Blowing an asteroid needs a lot of energy because, first, it must be cracked in multiple pieces, and then, those pieces need kinetic energy to be moved away from the asteroid's center.
Moving the asteroid, needs less energy. And It needs a very very little amount of energy if it's on the apoaxis of the orbit.
A nuke in the vacuum has a very large heating power, but don't produces large amounts of kinetic energy.
A solar sail will provide a larger amount of kinetic energy, but it would need just a larger time intervall (days instead of the few seconds of the nuke explosion)
