Answer
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Step-by-step explanation
The major thing wrong with Hermione's reasoning is that she did the calculations wrongly. Although, she wanted √34, and she started with
5.6 × 5.6 = 31.36 (She got 31.6, this is her first mistake, but this isn't the most crucial mistake)
Then,
5.7 × 5.7 = 32.49 not 34.29 (This is her most crucial mistake as she must have written th answer wrongly)
A better and more approximate guess will be
5.8 × 5.8 = 33.64
Since
5.9 × 5.9 = 34.81 and is farther from 34 than 33.61.
So, the error in her reasoning is a calculation error.
Hope this Helps!!!