(CNN) Elizabeth Warren showed in CNN's town hall Monday night how nimble and persuasive she can be as she wades deeper into policy specifics than other Democratic presidential contenders.

The Massachusetts senator's passion, her smooth performance and her substantive policy explanations showed why she's a formidable contender in this crowded field and why very few people would count her out, even if she's dragging in the polls. Here are three takeaways from the town hall:

Tackling that student loan price tag

With her sweeping student loan forgiveness proposal , Warren is making a strong play for young voters who Vermont Sen. Bernie Sanders won over during the 2016 election.

If the response the Massachusetts senator got at CNN's town hall with young voters was a good barometer, it's going over very well so far with students. "This is about opportunity for everyone," she said to applause Monday night.

But the bigger question for Warren going forward is whether she can defend the stunning $1.25 trillion price tag of the proposal. She offered a pretty clean, understandable explanation of how she would do that Monday night by detailing one of the first policies she rolled out: the "wealth tax" or the "ultra-millionaire's tax." She explained that it's "two cents on every dollar of the great fortunes above $50 million dollars. So your 50 millionth and first dollar, you have to pay two cents on all the dollars after that."

"Here's the stunning part," she said. "If we put that two cent wealth tax in place on the 75,000 largest fortunes in this country -- two cents -- we can do universal child care for every baby, zero to five, universal pre-K, universal college, and knock back the student loan burden for 95% of our students and still have nearly a trillion dollars left over."

'That's what girls do'

Asked how she'd overcome the barrage of sexism that faced Hillary Clinton in 2016 and could await a female nominee against Trump in 2020, Warren recounted her decision to run against Republican then-Sen. Scott Brown in 2012 -- a race many Democrats who urged Warren to run thought she was likely to lose.

"All I can say is, Democrats, get a better message," she said.

Warren said that every time she saw a little girl while on the campaign trail, she kneeled to talk to them. "I would say 'hi, my name is Elizabeth, and I'm running for Senate because that's what girls do,'" she said. Then she asked the girls to pinky-promise they'd remember it. She's used the same line as a presidential candidate.

Warren said women face similar headwinds as presidential candidates.

"One might say you persist," she said. "Organize, build a grassroots movement, fight for working people. And that's how I'm going to be the first woman elected president of the United States."

Warren defends call to impeach Trump

Warren made waves last week as the first Democratic presidential candidate to call for impeachment proceedings in the wake of special counsel Robert Mueller's report on the Russia probe. On Monday, she pushed back against Democrats who have argued now -- 18 months from another presidential election -- isn't the time for Trump's impeachment.

"There is no political inconvenience exception to the United States Constitution," she said.

The Massachusetts senator argued that "if any other human being in this country had done what's documented in the Mueller report, they would be arrested and put in jail." She said how lawmakers react to the Mueller report will affect the health of American democracy during future presidencies, too.

And, she said, there isn't much left to investigate.

"If you've actually read the Mueller report, it's all laid out there. It's not like it's going to take a long time to figure that out. It's there," Warren said. "It's got the footnotes, it's got the points, it connects directly to the law. But this really is fundamentally: I took an oath to uphold the Constitution of the United States and so did everybody else in the Senate and in the House."

Warren also said she thinks the Department of Justice position that indictments cannot be brought against sitting presidents is "wrong."