Between which two integers does (\sqrt{8}) lie on the number line?

Correct answer: (2) and (3)

The direct answer is option A: \(\sqrt8\) lies between 2 and 3. To locate a square root, compare nearby perfect squares. Since \(2^2=4\) and \(3^2=9\), we have \(4<8<9\). Taking positive square roots gives \(2<\sqrt8<3\). Therefore, option A is correct. Option B, between 1 and 2, is wrong because numbers in that interval have squares between 1 and 4, while 8 is larger than 4. Option C, between 3 and 4, is wrong because \(\sqrt8<\sqrt9=3\). Option D, between 4 and 5, is even farther right and cannot work. Although \(\sqrt8\) is approximately 2.83, approximation is not necessary. The key is identifying the consecutive perfect squares surrounding 8. Memory cue: square the endpoint integers before deciding.