33023中３・平方根・計算問題・乗法の基本3

$\begin{eqnarray}(1)\;\;\sqrt{2\,}\times\sqrt{6\,}&=& \sqrt{2\,}\times\sqrt{2\times 3\,}\\[5pt] &=& \sqrt{2\,}\times\sqrt{2\,}\times\sqrt{3\,} \\[5pt] &=& \color{red}(\,\sqrt{2\,}\,)^{2}\color{black}\times\sqrt{3\,} \\[5pt] &=& \color{red}2\color{black}\times\sqrt{3\,}\\[5pt] &=& 2\sqrt{3\,}\end{eqnarray}\;\;$

答$2\sqrt{3\,}$

$\begin{eqnarray}(2)\;\;\sqrt{3\,}\times\sqrt{15\,}&=&\sqrt{3\,}\times\sqrt{3\times 5\,}\\[5pt]&=&\sqrt{3\,}\times\sqrt{3\,}\times\sqrt{ 5\,}\\[5pt]&=&\color{red}(\,\sqrt{3\,}\,)^{2}\color{black}\times\sqrt{ 5\,}\\[5pt]&=&\color{red}3\color{black}\times\sqrt{ 5\,}\\[5pt]&=&3\sqrt{ 5\,}\end{eqnarray}\;\;$

答$3\sqrt{5\,}$

$\begin{eqnarray}(3)\;\;\sqrt{6\,}\times \sqrt{30\,}&=&\sqrt{6\,}\times\sqrt{6\times 5\,}\\[5pt]&=&\sqrt{6\,}\times\sqrt{6\,}\times\sqrt{ 5\,}\\[5pt]&=&\color{red}(\,\sqrt{6\,}\,)^{2}\color{black}\times\sqrt{ 5\,}\\[5pt]&=&\color{red}6\color{black}\times\sqrt{ 5\,}\\[5pt]&=&6\sqrt{ 5\,}\end{eqnarray}\;\;$

答$6\sqrt{5\,}$

$\begin{eqnarray}(4)\;\;\sqrt{14\,}\times\sqrt{35\,}&=&\sqrt{2\times 7\,}\times\sqrt{5\times 7\,}\\[5pt]&=&\sqrt{2\,}\times\sqrt{7\,}\times\sqrt{5\,}\times\sqrt{7\,}\\[5pt]&=&\color{red}(\,\sqrt{7\,}\,)^{2}\color{black}\times\sqrt{ 2\,}\times\sqrt{ 5\,}\\[5pt]&=&\color{red}7\color{black}\times\sqrt{10\,}\\[5pt]&=&7\sqrt{ 10\,}\end{eqnarray}\;\;$

答$7\sqrt{10\,}$

$\begin{eqnarray}(5)\;\;\sqrt{15\,}\times\sqrt{45\,}&=&\sqrt{15\,}\times\sqrt{15\times 3\,}\\[5pt]&=&\sqrt{15\,}\times\sqrt{15\,}\times\sqrt{3\,}\\[5pt]&=&\color{red}(\,\sqrt{15\,}\,)^{2}\color{black}\times\sqrt{3\,}\\[5pt]&=&\color{red}15\color{black}\times\sqrt{3\,}\\[5pt]&=&15\sqrt{ 3\,}\end{eqnarray}\;\;$

答$15\sqrt{3\,}$