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a)
\(7\sqrt{12}+\frac{1}{3}\sqrt{27}-\sqrt{75}\)
\(=14\sqrt{3}+\sqrt{3}-5\sqrt{3}\)
\(=10\sqrt{3}\)
b)
\(\left(2\sqrt{20}+\sqrt{125}-3\sqrt{80}\right):5\)
\(=\left(4\sqrt{5}+5\sqrt{5}-12\sqrt{5}\right):5\)
\(=-3\sqrt{5}:5\)
\(=\frac{-3\sqrt{5}}{5}\)
c)
\(3\sqrt{12a}-5\sqrt{3a}+\sqrt{48a}\)
\(=6\sqrt{3a}-5\sqrt{3a}+4\sqrt{3a}\)
\(=5\sqrt{3a}\)
a: \(=9\sqrt{2}-4\sqrt{2}+4\sqrt{2}+9\sqrt{2}=18\sqrt{2}\)
b: \(=8\sqrt{3}-12\sqrt{3}+5\sqrt{3}+2\sqrt{3}=3\sqrt{3}\)
c: \(=2\sqrt{21}\)
Bài 1:
a. \(\sqrt{\frac{25m^2}{49}}=\frac{\sqrt{25m^2}}{\sqrt{49}}=\frac{5m}{7}\)
b. \(\frac{\sqrt{192k}}{\sqrt{3k}}=\sqrt{\frac{192k}{3k}}=\sqrt{64}=8\)
Bài 2:
a. \(\frac{a+\sqrt{a}}{\sqrt{a}}=\frac{\left(\sqrt{a}\right)^2+\sqrt{a}}{\sqrt{a}}=\frac{\sqrt{a}\left(\sqrt{a}+1\right)}{\sqrt{a}}=\sqrt{a}+1\)
b. \(\frac{\sqrt{a}-a}{\sqrt{a}-1}=\frac{\sqrt{a}-\left(\sqrt{a}\right)^2}{\sqrt{a}-1}=\frac{\sqrt{a}\left(1-\sqrt{a}\right)}{\sqrt{a}-1}=\frac{-\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}=-\sqrt{a}\)
c. \(\frac{a-b}{\sqrt{a}-\sqrt{b}}=\frac{\left(\sqrt{a}\right)^2-\left(\sqrt{b}\right)^2}{\sqrt{a}-\sqrt{b}}=\frac{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}{\sqrt{a}-\sqrt{b}}=\sqrt{a}+\sqrt{b}\)