If \(u=-2-\sqrt{7}\) is represented on the number line, in which interval does \(u\) lie?

Correct answer: Between \(-5\) and \(-4\)

Since \(\sqrt{7}\approx 2.646\), we get \(u=-2-2.646\approx -4.646\). Therefore, \(u\) lies between \(-5\) and \(-4\). Note that subtracting a positive number from a negative number makes the result more negative, so it cannot lie between \(-4\) and \(-3\). In an exam, estimate the square root first and then locate the resulting number between consecutive integers.