Disclaimer: Harry Potter's not mine. J.K. Rowling owns him.
Harry and Ron couldn't believe it. Hermione Granger, miss goody-two-shoes, miss ooh-ooh-I-know-the-answer, had lied to a teacher. They were walking back to their common room in a slight daze not only from the near death experience of a raging troll but from the fact that The Hermione Granger had lied to a teacher. As they neared the portrait of the Fat Lady, they saw Hermione waiting for them.
"Blimey, thanks Hermione. I thought McGonagall was going to kill us," Ron said.
Harry nodded his agreement.
Hermione blushed and replied, "No, thank you for coming to find me. If it wasn't for you two, I might be dead now."
Ron and Harry stared at each other waiting for one of them to ask the question. Ron, ever impatient, gave in first and turned back to Hermione.
"I just can't believe that you lied to a teacher. I didn't think you had it in you."
"Yeah, me neither," Harry added.
Hermione crossed her arms in front of her and glared at the two boys as Ron continued.
"I mean you're always raising your hand right away to answer any of the teacher's questions. You got mad at us for breaking the rules that night when we saw that three-headed dog."
Harry saw Hermione's glare deepen towards Ron's direction, so he quickly punched Ron in the shoulder.
"Hey, what was that for?" Ron said as he rubbed his shoulder.
"I think she gets the idea," Harry replied.
Hermione sighed in exasperation. "Just because I like to do well in school and not get detentions or, even worse, expelled, doesn't mean that I wouldn't lie to a teacher. After all, they lie to us, so we should be able to lie to them."
Hermione's face darkened as she recalled horrific memories of Year 5 of Primary school. Ron and Harry looked at each other in confusion. This time Harry, surprisingly, gave in first.
"When have they lied to us?"
Hermione looked back at them shaking off the memories. "Are you sure you want to know? I've tried explaining it to other kids, but they don't seem to understand."
Harry and Ron both nodded.
"Alright, then. I'll try and explain it. Since the threat from the troll is gone, we can just go to an empty classroom.
The three children walked quickly through the hallways. Harry and Ron were bursting with the desire to know what was up with Hermione. This was a side of her they had never seen before, and they wanted to know what was going on. They finally reached an empty classroom. Dust and cobwebs filled the room. Obviously, it hadn't been used in awhile. Closing the door, Hermione walked up to the front of the room and started her story.
"It all started when I was in Year 5 of Primary school…"
Little Hermione Granger sat in the front of the classroom of course. It was the closest to the teacher, and she didn't have to look at some of the kids in the class who hated her. Some of the worst kids didn't participate at all, so Hermione could imagine that they weren't even in her class. The teacher stood in front of the blackboard as she wrote down the square root of nine.
"So, class, what would the square root of nine be?"
Hermione's hand immediately shot up. The teacher looked around, but no one else was raising their hand. She sighed.
"Yes, Hermione?"
"The answer is three."
"Good job, Hermione." The teacher said as she wearily smiled at her. She looked around at her other students and saw most of them eyeing the clock.
"Now class, just because it's almost time for lunch doesn't mean you shouldn't participate. I'm sure you're all hungry, but it's not lunch time yet so pay attention. Now, are they any questions about square roots?
Hermione's hand immediately shot up again.
"Yes, Hermione?"
Most of the class groaned. Once again, Hermione Granger would prolong their torture of Mathematics, and perhaps even make them stay a few minutes behind wasting precious minutes that could be used for lunch.
Hermione ignored the groans. "What about negative numbers? What would the square root of negative nine be?"
"Ah, good question, Hermione. So, class, anyone know the answer?"
No one raised their hand. A couple of kids in the back even put their heads down in boredom.
"Thomas! Jessica! Heads up, please. Now, the answer to your question, Hermione, is that it can't be done. Why's that? Well, think about how we've done it for other numbers. What multiplied by itself is equal to nine? Three, so the square root of nine is three, but nothing multiplied by itself is equal to negative nine. You could have three multiplied by negative three, but three is not equal to negative three, so the square root of negative nine can't be done. This is true for any negative number. Taking the square root of a negative number is impossible to do."
Hermione's face darkened in rage. "I remember that sentence being said so clearly. 'Taking the square root of a negative number is impossible to do.'"
Hermione seemed lost in the memory as she started repeating the word "impossible" to herself. She said it a number of different ways. Perhaps hoping if said correctly, it would change the meaning of the word.
Ron cleared his throat. "Uh, Hermione…"
Hermione's face shot up. "LIES! ALL LIES!" she screamed at the two boys in front of her.
Harry and Ron instinctively took a step back in fear.
Harry's brow furrowed in confusion. "Um, Hermione. I remember learning that too. My teacher also told us that taking the square root of a negative number is impossible to do. I don't understand what's wrong."
Ron, having never even heard of these square-whatsits, just nodded his head sagely as if Harry had said something obviously true.
"Your teacher was lying to you, Harry, just as mine was. Obviously, your aunt and uncle are not like my parents."
Usually, only one of Hermione's parents would be able to pick her up from school. Owning their own dentistry, one of them needed to stay behind to take care of the appointments in the late afternoon. The other would pick up their daughter from school and take her home. Today, however, was Friday, and sometimes on a Friday, they could close up their business early and go pick up their daughter together. Today was one of those Fridays.
Hermione spotted her parents' car near the end of the line of cars waiting in front of the school. She rushed over, opened the back door, and climbed into the car.
"Hi, mommy and daddy." Hermione said as she buckled up. Never go anywhere in a car without buckling up, her parents always told her.
"Hello, honey. How was your day?" Hermione's mother replied as she started the car back up.
Usually, during the twenty minute ride home, Hermione would explain to her parents all about what she had learned in school that day. Today was no different as Hermione went straight into the topic of reptiles and the things she had learned in Science.
About seven minutes into the car ride, Hermione went from talking about what she had learned in History to what she had learned in Mathematics.
"And then in Mathematics, we learned about square roots."
Hermione's father smiled as the day he had been dreaming about ever since he learned the dreaded truth was here.
"So let's test you. What's the square root of one hundred?"
"Ten," Hermione replied, smiling with success.
"Okay, what about the square root of negative sixteen?"
"Daddy! That's impossible."
Hermione's father smiled even further. His face looked like a cat ready to pounce on his prey.
"Actually, it's 4i."
Hermione's jaw dropped, and her eyes widened in surprise. Her father couldn't help it and started laughing.
Hermione's mother hit her father in the shoulder. "Dear, don't laugh at Hermione."
"I'm sorry. You should see her face though. Actually, don't. You're driving."
Hermione started sputtering. "But…the teacher said…"
Her father smiled back. "Ah, that's just what they tell kids when they're first learning this stuff. You'll learn about imaginary numbers when you're older."
Hermione's mother sighed and said, "Henry, you know how Hermione is. She won't wait 'til she's older. Since you started this, try to explain it to her now."
"Well, that's what we get for raising a genius of a daughter," Hermione's father replied.
Hermione looked back and forth between her parents in confusion. Shocked so badly, all she could do was stare back at her father as he explained about imaginary numbers.
"It's actually pretty simple. You see, the i is basically just the square root of negative one. So, when I said 4i, you could take it as four times the square root of negative one. What I did was take out a negative one from the negative sixteen. The square root of negative sixteen is equal to the square root of sixteen times the square root of negative one. The square root of sixteen is four, and the square root of negative one is i, so the final answer is 4i. Do you understand honey?"
Hermione understood alright. She understood that her teacher had lied to her and the rest of the class. Taking the square root of a negative number was possible to do. Hermione's face scrunched up, and she burst into tears.
Her father looked back in concern. "Hermione, what's wrong?"
Hermione's hands clenched into fists. Her face radiated hurt and rage from the offense of that Year 5 teacher. Harry and Ron instinctively took another step back, ready for another outburst from the girl in front of them.
"Do you see, Harry, Ron? That bloody teacher lied to me. She lied to all of us. I was bed-ridden for almost a week after that. If she didn't tell us about imaginary numbers, what else did she not tell us about? What else did the other teachers not tell us about? I trusted them to teach us, but they lied. They all bloody lied."
Hermione started pacing back and forth as she continued her rant.
"I went to my parents, but they told me that it was common to not tell children everything. Not until they were older when it could be more useful or they could finally understand. I went to the headmaster, but all he said was that if I wanted I could skip a year since I was so smart. Didn't he understand? I didn't want to skip a year just to go to another class filled with half-truths. I wanted them to stop lying."
Hermione stopped pacing and looked back at Harry and Ron.
"Ever since then, I haven't trusted any of the teachers. I still love learning and doing well in school, but I also read more advanced books on the subjects that we're learning. For example, you remember how Professor Flitwick was telling us how important it is to speak the incantation clearly otherwise we wouldn't be able to cast the spell? Well, I read later something he didn't tell us. It's possible to cast spells silently. Imagine that, casting spells without speaking the incantation. Did Professor Flitwick tell us this little nugget of information? No, he didn't. Why? Because we don't learn about silent spell casting until sixth year. That's why."
Professor Flitwick's omission seemed particularly offensive to Hermione as she started pacing again, looking skyward as if she were asking some higher power how this could be.
"We should have been told from the beginning that spells are first learned through vocalization of an incantation and some movement of the wand. Then, after doing the spell so many times and gaining familiarity with it, we can cast the spells without vocalization. We can do it by just thinking an incantation and moving the wand. Finally, we can even go a step above that if we are powerful enough. We can cast the spell without the wand, though only a few are capable of it."
Hermione stopped pacing again and glared at the two boys. She furiously pointed a finger at them. In her rage, she couldn't keep her finger from shaking.
"Did they tell us all of this when we first learned about casting spells? No, because apparently it would have been useless to us until we are older. Well, I say this omission of information is a travesty, a bloody travesty."
Hermione lowered her finger and tried breathing a deep, calming breath.
"I'm sorry. I get a little emotional about this. But, do you understand now?"
Not having one clue what that entire rant was about, but not wanting to invoke Hermione's wrath again, Ron quickly nodded. "Of course we understand, right Harry?"
Harry, on the other hand, did slightly understand. He still couldn't see what was so offensive about not telling children things that could wait until they were older, but he didn't want to invoke Hermione's wrath either so he nodded his head slowly. "Yeah, it's perfectly understandable."
Hermione smiled back at the two of them. "Thank you for understanding. Do you want to help me find other information the teachers aren't telling us? And, I could tell you all about the stuff I learned so far."
"Uh…sure," Harry replied, deciding it best not to upset her.
Ron almost threw Harry a look of complete disgust at the idea of studying more, but the memory of Hermione's rant stopped him. Instead, he just nodded his head in agreement.
A/N: I've been reading fanfiction for awhile now, but I haven't written much before. I had this idea spring into my head, so I decided to try writing it out. I'm American if you couldn't tell already, so I don't use proper English, but I did try. I even did some research on the school system in the U.K., though I couldn't find when you learned square roots, so I just made an educated guess. I remember memorizing the multiplication table in third grade, so square roots would probably be third or fourth grade. That translates to Year 4 or Year 5 in the U.K.'s school system I believe. If anyone knows the actual year, then maybe I'll change it. I kind of like the idea of where this could go and what might change because of Hermione's distrust of teachers not telling the whole truth. Plus, it would be interesting to see the effects of this distrust with Dumbledore not telling Harry the prophecy until the end of fifth year. I don't know if I'll continue with the idea, so if anyone wants to run with it, go for it.