Question: Dealing with constant 'why' phase from 4yo

So my daughter is in full interrogation mode and I'm losing my mind. Every single thing requires an explanation now. "Why is the sky blue?" "Why do we have to eat vegetables?" "Why do birds have feathers?" "Why why why?"

I don't want to shut her down because I know curiosity is good, but my brain is fried by 3pm. Anyone else dealing with this? How do you handle it without going insane? Do you just answer everything or is it okay to sometimes say "good question, let's look it up later"?