Giải bài 70 trang 40 – SGK Toán lớp 9 tập 1

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Áp dụng liện hệ giữa phép nhân và phép khai phương.

  $\begin{aligned} a)\,\sqrt{\dfrac{25}{81}.\dfrac{16}{49}.\dfrac{196}{9}}&=\dfrac{\sqrt{25}}{\sqrt{81}}.\dfrac{\sqrt{16}}{\sqrt{49}}.\dfrac{\sqrt{196}}{\sqrt{9}} \\ & =\dfrac{5}{9}.\dfrac{4}{7}.\dfrac{14}{3}=\dfrac{40}{27} \\ \end{aligned}$

 $\begin{aligned} b)\,\sqrt{3\dfrac{1}{16}.2\dfrac{14}{25}.2\dfrac{34}{81}}&=\sqrt{\dfrac{49}{16}.\dfrac{64}{25}.\dfrac{196}{81}} \\ & =\dfrac{\sqrt{49}}{\sqrt{16}}.\dfrac{\sqrt{64}}{\sqrt{25}}.\dfrac{\sqrt{196}}{\sqrt{81}} \\ & =\dfrac{7}{4}.\dfrac{8}{5}.\dfrac{14}{9}=\dfrac{196}{45} \\ \end{aligned}$
   $\begin{aligned} c)\,\dfrac{\sqrt{640}.\sqrt{34,3}}{\sqrt{567}}&=\sqrt{\dfrac{640.34,3}{567}}=\sqrt{\dfrac{64.343}{567}} \\ & =\sqrt{\dfrac{64.49}{81}}=\dfrac{\sqrt{64}.\sqrt{49}}{\sqrt{81}} \\ & =\dfrac{8.7}{9}=\dfrac{56}{9} \\ \end{aligned}$
  $\begin{aligned} d)\,\sqrt{21,6}.\sqrt{810}.\sqrt{{{11}^{2}}-{{5}^{2}}}&=\sqrt{21,6.810.\left( 11-5 \right)\left( 11+5 \right)} \\ & =\sqrt{216.81.6.16} \\ & =\sqrt{{{36}^{2}}{{.9}^{2}}{{.4}^{2}}} \\ & =36.9.4=1296 \\ \end{aligned}$