If point (P) has coordinate ( -\sqrt{48} ) on the number line, between which two consecutive integers does (P) lie?

Correct answer: (-7) and (-6)

The point has coordinate \\( -\sqrt{48} \\). To locate it, compare 48 with nearby perfect squares: \\(6^2=36\\) and \\(7^2=49\\). Therefore \\(6<\sqrt{48}<7\\). Taking the negative changes the order on the number line, so \\(-7<-\sqrt{48}<-6\\). Thus the point lies between the consecutive integers \\(-7\\) and \\(-6\\), which is option A. A common mistake is to choose 6 and 7 because the square root itself lies there, without considering the negative sign.

The value is approximately \\(-6.93\\), confirming the interval. The negative of a number between 6 and 7 must lie between -7 and -6, not between -6 and -5. The endpoint values are not included because \\(48\\) is not a perfect square, so the inequalities are strict. Hence the supplied answer A follows directly from comparing perfect squares and reversing the order correctly for negative numbers.