Question

The value of 12−−√ lies between which two consecutive integers?

Answer 1

You mean \( \sqrt{12} \) ?
Well for any integer you have: \( n = \sqrt{n^2} \)
So this question equates to finding the nearest perfect square below 12 and above 12. Those are numbers which have integer square roots. Does that make sense?

Answer 2

\( \sqrt{a^2} < \sqrt{12} < \sqrt{b^2} \) <-- a^2 < 12 < b^2
is equivalent to
\( a < \sqrt{12} < b \) <-- a, b are the integers we want.