a) Ta có: \(\sqrt{0.1}\cdot\sqrt{4000}\)
\(=\sqrt{\frac{1}{10}}\cdot\sqrt{4000}\)
\(=\sqrt{\frac{1}{10}\cdot4000}=\sqrt{400}=20\)
b) Ta có: \(\sqrt{\frac{9}{196}}=\sqrt{\left(\frac{3}{14}\right)^2}\)
\(=\left|\frac{3}{14}\right|\)
\(=\frac{3}{14}\)(Vì \(\frac{3}{14}>0\))
c) Ta có: \(\sqrt{16}\cdot\sqrt{36}-\sqrt{125}:\sqrt{0.01}\)
\(=\sqrt{16\cdot36}-\frac{\sqrt{125}}{\sqrt{\frac{1}{100}}}\)
\(=\sqrt{576}-\sqrt{125:\frac{1}{100}}\)
\(=24-\sqrt{125\cdot100}\)
\(=24-\sqrt{12500}\)
\(=24-50\sqrt{5}\)
d) Ta có: \(\left(\sqrt{112}-\sqrt{63}+\sqrt{7}\right):\sqrt{7}\)
\(=\left(4\sqrt{7}-3\sqrt{3}+\sqrt{7}\right):\sqrt{7}\)
\(=\frac{2\sqrt{7}}{\sqrt{7}}=2\)
e) Ta có: \(\sqrt{2.5}\cdot\sqrt{30}\cdot\sqrt{48}\)
\(=\sqrt{\frac{5}{2}\cdot30\cdot48}=\sqrt{3600}=60\)
