| # how to use | |
| ``` | |
| messages = [ | |
| {"role": "system", "content": system_prompt}, | |
| {"role": "user", "content": "What is the sqrt of 101?"}, | |
| ] | |
| text = tokenizer.apply_chat_template( | |
| messages, | |
| add_generation_prompt = True, # Must add for generation | |
| tokenize = False, | |
| ) | |
| from transformers import TextStreamer | |
| _ = model.generate( | |
| **tokenizer(text, return_tensors = "pt").to("cuda"), | |
| max_new_tokens = 1024, # Increase for longer outputs! | |
| # Recommended Gemma-3 settings! | |
| temperature = 1.0, top_p = 0.95, top_k = 64, | |
| streamer = TextStreamer(tokenizer, skip_prompt = True), | |
| ) | |
| ``` | |
| # expected output | |
| ``` | |
| <start_working_out> | |
| To find the square root of of of 101, | |
| we proceed by estimation or calculation. | |
| Estimation doesn't need the precision of of to be as exact as the calculation, but we'll use approximation methods first: | |
| 101 is just slightly more than 10 since \(10^2=100\) | |
| That helps us realize that \(\sqrt{101}\) is close to 10. | |
| When estimating, we can say: | |
| \[ | |
| \sqrt{101} \approx 10 | |
| Squaring both sides, we get: | |
| \[ 10^2 = 100 \] | |
| and | |
| \[ (\sqrt{101}) \approx 10 | |
| \] | |
| Now using reverse operation, square root of-1 can create -10: | |
| \[ | |
| \sqrt{-101} \approx -1 \times \sqrt{101} | |
| \] | |
| However, square roots of refer only to non-negative real numbers, thus this step also needs correction to fit our initial estimation: | |
| - The estimation suggests \(\sqrt{101} \approx 10 | |
| Re-evaluating for an exact answer gives us closer value to check again with square formation. Because \(10^2 = 100\), | |
| we see, | |
| \[ | |
| \sqrt{101} \approx 10. | |
| Finally, recognizing \(\sqrt{101}\) as approximately 10 satisfies \(10<sup>10\) | |
| Hence, the precise estimate: | |
| <end_working_out> | |
| <SOLUTION> \(\sqrt{101} \approx 10.\</SOLUTION><|im_end|> | |
| ``` | |