Tính:
\(\sqrt{1\frac{9}{16}}.5\frac{4}{9}.0.01\)
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\(b,\left(\sqrt{1\frac{9}{16}-\sqrt{\frac{9}{16}}}\right):5\)
\(=\left(\sqrt{\frac{25}{16}-\frac{3}{4}}\right):5\)
\(=\sqrt{\frac{13}{16}}:5\)
\(=\frac{\sqrt{13}}{4}:5\)
\(=\frac{\sqrt{13}}{20}\)
a) \(10\sqrt{0,01}.\sqrt{\frac{16}{9}}+3\sqrt{49}-\frac{1}{6}\sqrt{4}\)
\(=10\sqrt{\frac{10}{100}}.\sqrt{\frac{4^2}{3^2}}+3.\sqrt{7^2}-\frac{1}{6}\sqrt{2^2}\)
\(=10.\frac{\sqrt{10}}{10}.\frac{4}{3}+3.7-\frac{1}{6}.2\)
\(=\frac{4\sqrt{10}}{3}+27-\frac{1}{3}\)
\(=\frac{4}{3}\sqrt{10}+\frac{80}{3}\)
b) \(\left(1+\frac{2}{3}-\frac{1}{4}\right).\left(0,8-\frac{3}{4}\right)^2\)
\(=\frac{17}{12}.\left(\frac{4}{5}-\frac{3}{4}\right)^2\)
\(=\frac{17}{12}.\left(\frac{1}{20}\right)^2\)
\(=\frac{17}{12}.\frac{1}{400}\)
\(=\frac{17}{4800}\)
\(M=4\frac{1}{3}-\sqrt{16}+5\sqrt{\frac{4}{9}}-\frac{25}{\left(\sqrt{6}\right)^2}\)
\(=\frac{13}{3}-4+5\cdot\frac{2}{3}-\frac{25}{6}\)
\(=\frac{1}{3}+\frac{10}{3}-\frac{25}{6}\)
\(=\frac{11}{3}-\frac{25}{6}\)
\(=-\frac{1}{2}\)
\(0,5\sqrt{100}-\sqrt{\frac{4}{25}}=0,5.10-\frac{\sqrt{4}}{\sqrt{25}}=5-\frac{2}{5}=\frac{23}{5}=\frac{138}{30}\)
\(\left(\sqrt{1\frac{1}{9}-\sqrt{\frac{9}{16}}}\right):5=\left(\sqrt{\frac{10}{9}-\frac{3}{4}}\right):5=\sqrt{\frac{13}{36}}:5=\frac{\sqrt{13}}{6}:5=\frac{\sqrt{13}}{30}\)
Vì 13 < 138 nên \(\sqrt{13}< 138\Rightarrow\frac{\sqrt{13}}{30}< \frac{138}{30}\)
Vậy \(0,5\sqrt{100}-\sqrt{\frac{4}{25}}>\left(\sqrt{1\frac{1}{9}-\sqrt{\frac{9}{16}}}\right):5\).