If \(x=\sqrt{a}\) and \(12.6<x<12.7\) on the number line, which value of \(a\) is possible?

Correct answer: \(159\)

Since \(x\) is positive, squaring the inequality gives \(12.6^2<a<12.7^2\). Therefore, \(158.76<a<161.29\). Among the given options, only \(159\) lies in this interval. The value \(158\) is too small, while \(162\) and \(163\) are too large. Exam tip: For \(x=\sqrt a\), square the bounds on \(x\) to find the required interval for \(a\).