The first option uses a correct idea (i.e. [tex] \sqrt{9}<\sqrt{13}<\sqrt{16} [/tex]) to deduce that [tex] 3<\sqrt{13}<4 [/tex], but then states something false, because [tex] 3.1^2 = 9.61 [/tex].
The second option is completely wrong: [tex] \sqrt{13}<\sqrt{16} [/tex] is true, but this means that [tex] \sqrt{13}<4[/tex], not greater.
The third option is correct, because it applies the correct logic of the first option, but the computation is correct this time.
The fourth option is wrong because [tex] \sqrt{13} [/tex] is not between 12 and 14.
