"establish precisely" is a correct and usable phrase in written English.
You can use it to emphasize that something should be done in an exact way. For example, "We need to establish precisely what our priorities are for this project."
The prime minister, Jean-Pierre Raffarin, ordered an official inquiry to establish precisely how many people died in the exceptional temperatures during the first half of August.
Ms. Salac said F.A.A. inspectors would investigate Continental's preflight maintenance procedures and establish precisely what the mechanic did before the jet lurched.
We're already working with the University to establish precisely how this information got through our extensive security proceedures and to ensure there can be no repeat".
The preliminary investigation also failed to establish precisely what caused the attack, and in particular whether the American planes had been the target of antiaircraft fire.
The count is continuing to establish precisely the final margin Malcolm Turnbull will be able to claim as prime minister, and the character of the Senate his government will ultimately have to deal with.
"It is probably impossible now to establish precisely what was said or understood on each side in conversations between Mark Thompson and Sir Michael Lyons at the time," said Patten.
In the decades since the clinic was established, precisely no reproducible results have emerged.
But it has not established precisely what set off the tank, according to investigators.
"It establishes precisely the kind of system that the United States has consistently urged other countries not to adopt.
Neither side is willing to initiate the much-needed call on the bilateral hotline established precisely for this type of situation.
They walked coolly around Twickenham, establishing precisely what each player would do in every foreseeable situation in every part of the pitch.
