C1. Tính:a) \(\left(3\sqrt{\frac{3}{5}}-\sqrt{\frac{5}{3}}+\sqrt{5}\right)2\sqrt{5}+\frac{2}{3}\sqrt{75}\)b) \(\left(\sqrt{3}-1\right)^2-\sqrt{\left(1-\sqrt{3}\right)^2}+\sqrt{\left(-3\right)^2.3}\)C2. TínhP = \(\frac{a-b}{\sqrt{a}+\sqrt{b}}+\frac{a\sqrt{a}-b\sqrt{b}}{a+b+\sqrt{ab}}\) , \(a\ge0,b\ge0,a\ne...
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C1. Tính:
a) \(\left(3\sqrt{\frac{3}{5}}-\sqrt{\frac{5}{3}}+\sqrt{5}\right)2\sqrt{5}+\frac{2}{3}\sqrt{75}\)
b) \(\left(\sqrt{3}-1\right)^2-\sqrt{\left(1-\sqrt{3}\right)^2}+\sqrt{\left(-3\right)^2.3}\)
C2. Tính
P = \(\frac{a-b}{\sqrt{a}+\sqrt{b}}+\frac{a\sqrt{a}-b\sqrt{b}}{a+b+\sqrt{ab}}\) , \(a\ge0,b\ge0,a\ne b\)
\(a,\left(3\sqrt{\frac{3}{5}}-\sqrt{\frac{5}{3}}+\sqrt{5}\right)2\sqrt{5}+\frac{2}{3}\sqrt{75}\)
\(=6\sqrt{3}-\frac{10\sqrt{3}}{3}+10+\frac{10\sqrt{3}}{3}\)
\(=6\sqrt{3}+10\)
\(b,\left(\sqrt{3}-1\right)^2-\sqrt{\left(1-\sqrt{3}\right)^2}+\sqrt{\left(-3\right)^2.3}\)
\(=\left(\sqrt{3}^2-2.\sqrt{3}.1+1^2\right)-|1-\sqrt{3}|+\sqrt{27}\)
\(=4-2\sqrt{3}-\sqrt{3}+1+3\sqrt{3}\)
\(=5\)
\(P=\frac{a-b}{\sqrt{a}+\sqrt{b}}+\frac{a\sqrt{a}-b\sqrt{b}}{a+b+\sqrt{ab}}\left(a\ge0;b\ge0;a\ne b\right)\)
\(=\frac{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{a}+\sqrt{b}}+\frac{\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b\right)}{a+b+\sqrt{ab}}\)
\(=\sqrt{a}-\sqrt{b}+\sqrt{a}-\sqrt{b}\)
\(=2\sqrt{a}-2\sqrt{b}\)