Áp dụng quy tắc khai phương một tích
1: Ta có: \(\sqrt{\frac{1}{5}}\cdot\sqrt{\frac{1}{20}}\cdot3\cdot7\)
\(=\sqrt{\frac{1}{5}}\cdot\sqrt{\frac{1}{20}}\cdot\sqrt{9}\cdot\sqrt{49}\)
\(=\sqrt{\frac{1}{5}\cdot\frac{1}{20}\cdot9\cdot49}\)
\(=\sqrt{\frac{441}{100}}=\frac{\sqrt{441}}{\sqrt{100}}=\frac{21}{10}\)
2: Ta có: \(\sqrt{0,001\cdot360\cdot3^2\cdot\left(-3\right)^2}\)
\(=\sqrt{0,001}\cdot\sqrt{360}\cdot\sqrt{3^{^2}}\cdot\sqrt{\left(-3\right)^2}\)
\(=\sqrt{\frac{1}{100}}\cdot\sqrt{\frac{1}{10}}\cdot\sqrt{6^2}\cdot\sqrt{10}\cdot3\cdot3\)
\(=\frac{1}{10}\cdot6\cdot9\cdot\sqrt{\frac{1}{10}\cdot10}=\frac{54}{10}\cdot1=\frac{27}{5}\)
Áp dụng quy tắc nhân căn thức bậc hai
1: Ta có: \(2\sqrt{2}\left(4\sqrt{8}-\sqrt{32}\right)\)
\(=2\sqrt{2}\cdot4\sqrt{8}-2\sqrt{2}\cdot\sqrt{32}\)
\(=8\cdot\sqrt{16}-2\cdot\sqrt{64}\)
\(=8\cdot4-2\cdot8\)
=32-16=16