Translation:We have to go to study.
The correct sentence is given as "We've to go to study". That is not correct English. Have cannot be contracted when it is emphasized.
"We have to go study" is a much more idiomatic sentence than "We have to go to study."
I agree that "We have to go study" is what would normally be said. I think sometimes there is too much emphasis on word to word translation, which results in sentences that are a bit unnatural.
Maybe in US English. The latter is more natural for me as a British English speaker. It's good to have all the options out there though.