Which option correctly gives the position of (4-\sqrt{18}) on the number line?

Correct answer: Between ( -1 ) and (0)

The direct answer is option A: between \(-1\) and 0. Estimate the root using nearby squares: \(4^2=16\) and \(5^2=25\), and 18 is between them, so \(\sqrt{18}\) is a little greater than 4. In fact, \(\sqrt{18}\approx4.243\). Therefore \(4-\sqrt{18}\approx4-4.243=-0.243\). This number is negative but greater than \(-1\), so it lies between \(-1\) and 0. Option A is correct. Option B would require the result to be positive, but the root is greater than 4, making the subtraction negative. Option C and option D are positive intervals and therefore cannot contain the result. Notice that \(\sqrt{18}\) is not 18; confusing a root with the number inside it causes errors. Memory cue: first decide whether the root is larger or smaller than the number being subtracted, then estimate the interval.