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第115页

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$ \begin{aligned} 解:原式&=-\sqrt {60}×\sqrt {96} \\ &=-\sqrt {10×576} \\ &=-24 \sqrt{10} \\ \end{aligned}$

$ \begin{aligned} 解:原式&=2\sqrt {35×\frac {10}{7}} \\ &=\sqrt {100×2} \\ &=10\sqrt{2} \\ \end{aligned}$

$ \begin{aligned}解:原式&=\sqrt {\frac {8}{5}}×(-\sqrt {30}) \\ &=-\sqrt {16×3} \\ &=-4\sqrt{3} \\ \end{aligned}$

$ \begin{aligned}解:原式&=\sqrt {36m^3n^5} \\ &=\sqrt {36m^2n^4•mn} \\ &=6mn^2\sqrt{mn} \\ \end{aligned}$

$ \begin{aligned} 解:原式&=\sqrt {42}×\sqrt {-24} \\ &=-\sqrt {7×144} \\ &=-12\sqrt{7} \\ \end{aligned}$

$ \begin{aligned}解:原式&=4\sqrt {ab}•\sqrt {a(a^2-2ab+b^2)} \\ &=4\sqrt {ab}•\sqrt {a(a-b)^2} \\ &=4\sqrt {a^2(a-b)b} \\ &=4a(a-b) \sqrt{b} \\ \end{aligned}$

$ \begin{aligned} 解:根据题意得V&=4 \sqrt{18}×2\sqrt{27}×\frac 13\sqrt {60} \\ &=144\sqrt{10}. \\ \end{aligned}$

$答:这个长方体的体积为144\sqrt{10}.$

$\sqrt{6×8+1}=7$

$解: \sqrt{(n+1)(n+3)+1}=n+2， $

$ \begin{aligned}证明: \sqrt{(n+1)(n+3)+1}&= \sqrt{n^2+3n+n+3+1} \\ &=\sqrt{n^2+4n+4} \\ &=\sqrt{(n+2)^2} \\ &=n+2. \\ \end{aligned}$