33031中３・平方根・計算問題・除法の基本1

$\begin{array}{rcl}(1)\sqrt{15}÷\sqrt{3}& =& \frac{\sqrt{15}}{\sqrt{3}}\\ & =& \sqrt{\frac{15}{3}}\\ & =& \sqrt{5}\end{array}$

答$\begin{array}{r}\sqrt{5}\end{array}$

$\begin{array}{rcl}(2)\sqrt{30}÷(-\sqrt{6})& =& -\frac{\sqrt{30}}{\sqrt{6}}\\ & =& -\sqrt{\frac{30}{6}}\\ & =& -\sqrt{5}\end{array}$

答$\begin{array}{r}-\sqrt{5}\end{array}$

$\begin{array}{rcl}(3)-\sqrt{45}÷\sqrt{5}& =& -\frac{\sqrt{45}}{\sqrt{5}}\\ & =& -\sqrt{\frac{45}{5}}\\ & =& -\sqrt{9}\\ & =& -\sqrt{3^2}\\ & =& -3\end{array}$

$a>0$のとき$\begin{array}{r}\sqrt{a^2}=a\end{array}$

答$\begin{array}{r}-3\end{array}$

$\begin{array}{rcl}(4)\frac{\sqrt{75}}{\sqrt{3}}& =& \sqrt{\frac{75}{3}}\\ & =& \sqrt{25}\\ & =& \sqrt{5^2}\\ & =& 5\end{array}$

$a>0$のとき$\begin{array}{r}\sqrt{a^2}=a\end{array}$

答$\begin{array}{r}5\end{array}$

$\begin{array}{rcl}(5)-\frac{\sqrt{96}}{\sqrt{6}}& =& -\sqrt{\frac{96}{6}}\\ & =& -\sqrt{16}\\ & =& -\sqrt{4^2}\\ & =& -4\end{array}$

$a>0$のとき$\begin{array}{r}\sqrt{a^2}=a\end{array}$

答$\begin{array}{r}-4\end{array}$