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Answer: 44 and 45
Squaring numbers to get close to $2017$
$40^2=1600$ too small
$50^2=2500$ too big, so $\sqrt{2017}$ is between $40$ and $50$.
$45^2=2025$, very close but a bit too big
$44^2=1936$, too small, so $\sqrt{2017}$ is between $44$ and $45$.
Root 2017
Age 14 to 16
ShortChallenge Level 
Answer: 44 and 45
Squaring numbers to get close to $2017$
$40^2=1600$ too small
$50^2=2500$ too big, so $\sqrt{2017}$ is between $40$ and $50$.
$45^2=2025$, very close but a bit too big
$44^2=1936$, too small, so $\sqrt{2017}$ is between $44$ and $45$.
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