\(\begin{align}
& \sqrt{{{b}^{2}}+7bc+{{c}^{2}}}-(b+c)<\sqrt{abc}<\sqrt{{{b}^{2}}+7bc+{{c}^{2}}}+(b+c) \\
& \sqrt{\frac{b}{c}+7+\frac{c}{b}}-\sqrt{\frac{b}{c}+2+\frac{c}{b}}<\sqrt{a}<\sqrt{\frac{b}{c}+7+\frac{c}{b}}+\sqrt{\frac{b}{c}+2+\frac{c}{b}} \\
& \frac{5}{\sqrt{\frac{b}{c}+7+\frac{c}{b}}+\sqrt{\frac{b}{c}+2+\frac{c}{b}}}<\sqrt{a}<\sqrt{\frac{b}{c}+7+\frac{c}{b}}+\sqrt{\frac{b}{c}+2+\frac{c}{b}} \\
& 1=\frac{5}{\sqrt{2+7}+\sqrt{2+2}}<\sqrt{a}<\sqrt{2+7}+\sqrt{2+2}=5 \\
& 1<a<25 \\
\end{align}\)
