When Close Enough Is Close Enough

2? + V526 = 3. Teacher: Please show me your solution to this problem. Student: Sure. At first I was confused, but then I had a great idea. I just used my calculator. Both sides of the equation evaluate to 1.732050808. So they're the same! Teacher: Hmm. That's a good idea, but it doesn't really answer the question. You see, your calculator can display only 10 digits. It's possible that these two numbers agree to 10 decimal places, but aren't equal. Student: Get out! I don't believe that two expressions that agree to that many digits could be different. Teacher: Actually, they could. Let me give you an example. Do you have your calculator with you? Student: Yes. Teacher: Excellent. Please calculate