Tara Westover was a freshman in college when she first heard of the Holocaust.

“I don’t know this word,” she told a professor in class. “What does it mean?”

“There was a silence,” Westover writes in her memoir “Educated” (Random House), out Tuesday. “Not a hush, not a muting of the noise, but utter, almost violent silence . . . The professor’s lips tightened. ‘Thanks for that,’ he said, then returned to his notes.”

Westover’s ignorance was hardly her fault. She had been barred from school for her entire life. Her parents, strict fundamentalist Mormons, had raised their large family on an Idaho mountainside with few books and little interaction with the wider world.

How this unlettered girl zoomed to the heights of academia — a Harvard fellowship, a Cambridge Ph.D. — within the next decade would seem to be a tale of triumph, a portrait of the liberating power of a life of the mind.

For Westover, it’s not so simple.

Westover was born in the family home on Buck’s Peak in southeastern Idaho in 1986, the youngest of seven children. Her father, who nursed paranoid suspicions about the federal government and expected the end times to arrive at any moment, would not permit a hospital birth or reveal her existence to authorities.

She finally got a birth certificate nine years later. An older brother needed one to get a driver’s license and a job, and her father suddenly reversed his 10-year policy against them.

When they applied for it, state workers were flummoxed that no one in the family could agree on her actual birth date.

“Not knowing my birthday had never seemed strange,” Westover writes. “I knew I’d been born near the end of September, and each year I picked a day, one that didn’t fall on a Sunday because it’s no fun spending your birthday in church.”

She grew up pitching scrap in her father’s junkyard, canning peaches for his expansive post-apocalypse cache of food and keeping her “head-for-the-hills” bag packed and ready.

The mountain, a 7,457-foot peak, loomed as the family’s guardian and its touchstone. “I had been educated in the rhythms of the mountain, rhythms in which change was never fundamental, only cyclical,” she writes. “All my father’s stories were about our mountain, our valley, our jagged little patch of Idaho.”

“Government school,” as her father called it, was out of the question for his children: It would only brainwash them. Before Tara’s birth, her mother had planned to home-school them herself and collected an elementary science book, one book on American history and a handful of math textbooks.

On the rare days when young Tara “did school,” she admits, she “opened my math book and spent 10 minutes turning pages, running my fingers down the center fold. If my finger touched 50 pages, I’d report to Mother that I’d done 50 pages of math.”

“‘Amazing!’ she’d say. ‘You see? That pace would never be possible in the public school.’”

The family also rejected modern medicine. Her mother, an herbalist and self-trained midwife, treated the many injuries her children sustained doing heavy labor on the homestead. Herbal tinctures of juniper and mullein treated 10-year-old Tara when her leg was impaled by an iron bar as she worked in the family’s scrapyard, one of several incidents she recalls in cringeworthy detail.

The herbs couldn’t heal every wound. A highway wreck in their uninsured car left her mother with memory loss and dissociative episodes. A brother who tried to cut a gas tank off a junked car with a blowtorch was permanently scarred. Neither went to a hospital or saw a doctor.

One Sunday, Westover performed a choir solo in church, winning the praise of her congregation. As a result, her parents allowed her to pursue music, taking piano and dancing lessons — but even then her strict beliefs were a barrier.

“I thought they looked like tiny harlots,” she says of the other girls’ dance costumes at her first and only recital. She performed in a long gray sweatshirt that was still too immodest for her father’s liking.

“Although my family attended the same church as everyone in our town, our religion was not the same,” Westover writes. “I could stand with my family or with the gentiles . . . but there was no foothold in between.”

Most of her siblings began lives of patchy construction jobs and early marriages. Westover expected that she’d do the same, until her black-sheep brother Tyler convinced her that a music degree would let her become the town choir director someday.

Eight years Tara’s senior, Tyler had attended school before their father decided to withdraw the family from the world. Passionate about learning, he was self-directed enough to pursue it on his own, teaching himself trigonometry and calculus out of textbooks. When he went to college to study engineering, their father tried to lecture him into submission — but didn’t stand in his way when Tyler paid his own tuition and left the mountain.

‘There’s a world out there, Tara’

Five years later, on one of his rare visits home, Tyler took his sister aside.

“ ‘There’s a world out there, Tara,’ he said. ‘And it will look a lot different once Dad is no longer whispering his view of it in your ear.’ ”

Spurred on, Westover drove 40 miles to buy herself a trigonometry textbook and studied for the ACT out of her father’s view, signing up for it through a computer at a local business where she did bookkeeping. When she took it for the first time at age 16 in a nearby high school, she floundered, with no idea how to bubble in answers and no experience concentrating in a crowded classroom. “More than stupid, I felt ridiculous,” she writes.

On her second try, she earned a score high enough to qualify for entry into Brigham Young University, the Mormon Church’s college in Salt Lake City. Home-schooling families are common in the Mountain West region, and her application’s claim that she had studied rigorously for years under her mother’s supervision raised no eyebrows. She was accepted.

In 2004, she moved into an off-campus apartment and started classes at age 17, paying her own way with money she had earned through bookkeeping and grocery-clerk jobs. Her father had treated her with sullen silence once it became clear that she was leaving despite him. Her mother drove her to school and helped her move in.

Classes were a constant struggle for a student with poor study skills and next to no cultural literacy. Westover had never been taught to write an essay or take notes. As she read her textbooks, she had to stop repeatedly to research what she called “black-hole words”: terms she had never encountered, like the Enlightenment or the civil rights movement.

She was stunned when a US history class revealed ugly truths about racism and discrimination. The 1955 lynching of Emmett Till, she learned, had occurred only a few decades before, not in America’s distant past. “My proximity to this murdered boy could be measured in the lives of people I knew . . . in the lines on my mother’s face,” she realized.

Returning home that summer, her brother’s casual use of “n—-r” was suddenly intolerable to her. “The word and the way Shawn said it hadn’t changed,” she writes. “Only my ears were different.”

In Psychology 101, when her professor listed the symptoms of bipolar disorder — paranoia, mania, delusions of grandeur and persecution — it suddenly occurred to Westover that her dad was suffering from the condition. She used the pretext of a research paper to interrogate the university’s specialists and produced a damning project outlining the impact of bipolar parents on their children.

“I felt only anger,” she recalls. “We had been bruised and gashed and concussed . . . it was us who paid.”

But the academic revelation that had the greatest effect on Westover dated back to her very first days in the classroom. Her naïve question about the Holocaust first made her feel ashamed: “I didn’t raise my hand for the rest of the semester,” she writes. Shame turned to anger at her parents for allowing her to grow up so intellectually stunted.

By her junior year, anger had become a passionate hunger to expand her horizons. “I wanted a taste of that infinity,” she writes. She traded her music classes for geography, comparative politics and a course on Jewish history.

“By the end of the semester the world felt big,” she writes, “and it was hard to imagine returning to the mountain, to a kitchen or even to a piano.”

She found a mentor in her history professor, who asked her to apply to his study-abroad program at Cambridge University in England. Westover had never heard of Cambridge, but she won a spot nonetheless. She took out a student loan to pay the fees.

Her world grew that much bigger as she traveled abroad. “My imagination had never produced anything so grand,” she says of her first sight of the ancient King’s College on Cambridge’s campus.

There, she read historiography — the study of historians — with an eminent Holocaust expert, who guided her exploration of how researchers’ biases warp our understanding of the past. The project, inspired by her own experiences, was, the professor told her, one of the best he had read in his 30 years at Cambridge.

She returned to Brigham Young to complete her bachelor’s degree, graduating magna cum laude in 2008. During that final year, her Cambridge mentor helped her win the Gates Cambridge Scholarship, which fully funded her return to England to study for her master’s degree.

Her father disapproved. “Our ancestors risked their lives to cross the ocean, to escape those socialist countries. And what do you do? You turn around and go back?” he scolded. Her parents boycotted her graduation honors dinner and showed up late for her commencement.

Westover remained in touch with her family during her yearlong master’s program, and crossed the Atlantic several times for visits. But she felt increasing condemnation from her parents. When she won a graduate fellowship at Harvard, they came to see her — so that her father could perform an exorcism. “What my father wanted to cast from me wasn’t a demon,” she writes. “It was me.”

In 2010, Westover returned to Cambridge to pursue her Ph.D. as her family ties frayed. Most of her siblings cut off communications. She made one last trip back to Buck’s Peak — to retrieve the journals that form the basis of her book.

By 2014, when she earned her doctorate in history, she was close to three of her brothers, including the college-educated Tyler, and had made new connections with aunts and cousins who had themselves been estranged by her parents’ beliefs. But she chose to make an anguished peace with the rest of her family from afar.

“You can love someone and still choose to say goodbye to them,” she says now. “You can miss a person every day, and still be glad that they are no longer in your life.”