Câu 70 Trang 40: Biến đổi, rút gọn biểu thức

Ta có :

a.  $\sqrt{\frac{25}{81}.\frac{16}{49}.\frac{196}{9}}$

=  $\sqrt{\frac{25}{81}}.\sqrt{\frac{16}{49}}.\sqrt{\frac{196}{9}}$

=  $\frac{5}{9}.\frac{4}{7}.\frac{14}{3}=\frac{5.4.14}{9.7.3}=\frac{40}{27}$

Vậy  $\sqrt{\frac{25}{81}.\frac{16}{49}.\frac{196}{9}}=\frac{40}{27}$

b.   $\sqrt{3\frac{1}{16}.2\frac{14}{25}.2\frac{34}{81}}$

=  $\sqrt{\frac{49}{16}.\frac{64}{25}.\frac{196}{81}}$

=  $\sqrt{\frac{49}{16}}.\sqrt{\frac{64}{25}}.\sqrt{\frac{196}{81}}$

=  $\frac{7}{4}.\frac{8}{5}.\frac{14}{9}=\frac{196}{45}$

Vậy $\sqrt{3\frac{1}{16}.2\frac{14}{25}.2\frac{34}{81}}=\frac{196}{45}$

c.  $\frac{\sqrt{640}.\sqrt{34,3}}{\sqrt{567}}$

=  $\sqrt{\frac{640.34,3}{567}}$

=  $\sqrt{\frac{64.49}{81}}$

=  $\frac{\sqrt{64}.\sqrt{49}}{\sqrt{81}}$

=  $\frac{8.7}{9}=\frac{56}{9}$

Vậy $\frac{\sqrt{640}.\sqrt{34,3}}{\sqrt{567}}=\frac{56}{9}$

d.  $\sqrt{21,6}.\sqrt{810}.\sqrt{11^{2}-5^{2}}$

=  $\sqrt{21,6.810.(11^{2}-5^{2})}$

=  $\sqrt{216.81.(11+5)(11-5)}$

=  $\sqrt{36^{2}.9^{2}.4^{2}}=36.9.4=1296$

Vậy $\sqrt{21,6}.\sqrt{810}.\sqrt{11^{2}-5^{2}}=1296$