Answer: It's between 10 and 11
It's closer to 11 than it is to 10.
This is because [tex]\sqrt{113} \approx 10.63[/tex] after using a calculator.
You could also look at the list of perfect squares
{1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144,...}
The terms in bold are where 113 fits in between. So we can say,
[tex]100 < 113 < 121\\\\\sqrt{100} < \sqrt{113} < \sqrt{121}\\\\10 < \sqrt{113} < 11\\\\[/tex]
