Problem:
Simplify the following radical expression: $\left(\sqrt{70}-74\right)+\left(\sqrt{120}-\sqrt{56}\right)$.
Answer:
\begin{array}{l}
 
\begin{array}{l}
 \text{Simplify the following}: \\
 \sqrt{70}-74+\sqrt{120}-\sqrt{56} \\
\end{array}
 \\
\hline
 
\begin{array}{l}
 \sqrt{56} \text{= }\sqrt{2^3\times 7} \text{= }2 \sqrt{2} \sqrt{7}: \\
 \sqrt{70}-74+\sqrt{120}-\fbox{$2 \sqrt{2} \sqrt{7}$} \\
\end{array}
 \\
 
\begin{array}{l}
 \sqrt{2} \sqrt{7}=\sqrt{2\times 7}: \\
 \sqrt{70}-74+\sqrt{120}-2 \fbox{$\sqrt{2\times 7}$} \\
\end{array}
 \\
 
\begin{array}{l}
 2\times 7 \text{= }14: \\
 \sqrt{70}-74+\sqrt{120}-2 \sqrt{\fbox{$14$}} \\
\end{array}
 \\
 
\begin{array}{l}
 \sqrt{120} \text{= }\sqrt{2^3\times 15} \text{= }2 \sqrt{2} \sqrt{15}: \\
 \sqrt{70}-74+\fbox{$2 \sqrt{2} \sqrt{15}$}-2 \sqrt{14} \\
\end{array}
 \\
 
\begin{array}{l}
 \sqrt{2} \sqrt{15}=\sqrt{2\times 15}: \\
 \sqrt{70}-74+2 \fbox{$\sqrt{2\times 15}$}-2 \sqrt{14} \\
\end{array}
 \\
 
\begin{array}{l}
 2\times 15 \text{= }30: \\
 \fbox{$
\begin{array}{ll}
 \text{Answer:} &  \\
 \text{} & \sqrt{70}-74+2 \sqrt{\fbox{$30$}}-2 \sqrt{14} \\
\end{array}
$} \\
\end{array}
 \\
\end{array}
{'source': 'AMPS', 'file': 'amps/mathematica/algebra/simplify_radicals_w_steps/3187.txt'}