Question

Where would square root 113 be located on a number line

Answer 1

Answer: It's between 10 and 11

It's closer to 11 than it is to 10.

This is because $\sqrt{113} \approx 10.63$ 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,

$100 < 113 < 121\\\\\sqrt{100} < \sqrt{113} < \sqrt{121}\\\\10 < \sqrt{113} < 11$