\(\frac{1}{2}\sqrt{48}-2\sqrt{75}-\frac{\sqrt{33}}{\sqrt{11}}+5\sqrt{\frac{4}{3}}\)

\(=2\sqrt{3}-10\sqrt{3}-\sqrt{3}+\frac{10\sqrt{3}}{3}\)

\(=-9\sqrt{3}+\frac{10\sqrt{3}}{3}\)

\(=\frac{-27\sqrt{3}}{3}+\frac{10\sqrt{3}}{3}\)

\(=\frac{-17\sqrt{3}}{3}\)

\(\frac{1-a\sqrt{a}}{1-\sqrt{a}}\) \(=\frac{1^3-\left(\sqrt{a}\right)^3}{1-\sqrt{a}}\)

                            \(=\frac{\left(1-\sqrt{a}\right)\left(a+\sqrt{a}+1\right)}{1-\sqrt{a}}\)

                            \(=a+\sqrt{a}+1\)

chúc bn học tốt

\(\frac{1-a\sqrt{a}}{1-\sqrt{a}}\)

\(=\frac{\left(1-\sqrt{a}\right)\left(a+\sqrt{a}+1\right)}{1-\sqrt{a}}\)

\(=a+\sqrt{a}+1\)

\(=\frac{1}{2}\sqrt{48}-2\sqrt{75}-\frac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\frac{1}{3}}\)

\(=\frac{1}{2}4\sqrt{3}-2.5\sqrt{3}-\sqrt{3}+\frac{10}{\sqrt{3}}=-9\sqrt{3}+\frac{10}{\sqrt{3}}=\frac{-17\sqrt{3}}{3}\)

\(\frac{1}{2}\sqrt{48}-2\sqrt{75}-\frac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\frac{1}{3}}\)

=\(\frac{1}{2}\sqrt{3.4^2}-2\sqrt{3.5^2}-\sqrt{\frac{33}{11}}+5\sqrt{\frac{4}{3}}\)

\(=2\sqrt{3}-10\sqrt{3}-\sqrt{3}+10\sqrt{\frac{1}{3}}\)

\(=2\sqrt{3}-10\sqrt{3}-\sqrt{3}+\frac{10}{3}\sqrt{3}\)

\(=\left(2-10-1+\frac{10}{3}\right)\sqrt{3}\)

\(=\frac{-17}{3}\sqrt{3}\)

\(\sqrt{150}+\sqrt{1,6}.\sqrt{60}+4,5\sqrt{2\frac{2}{3}}-\sqrt{6}\)

\(=\sqrt{6.5^2}+\sqrt{96}+4,5\sqrt{\frac{8}{3}}-\sqrt{6}\)

\(=5\sqrt{6}+\sqrt{6.4^2}+4,5\frac{\sqrt{24}}{3}-\sqrt{6}\)

\(=5\sqrt{6}+4\sqrt{6}+\frac{4,5.2\sqrt{6}}{3}-\sqrt{6}\)

\(=8\sqrt{6}+3\sqrt{6}\)

\(=11\sqrt{6}\)

Tự hòi tự trl :D ?

\(\frac{1}{2}\sqrt{48}-2\sqrt{75}-\frac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\frac{1}{3}}\)

\(=\frac{1}{2}\sqrt{16.3}-2.5\sqrt{3}-\sqrt{3}-\frac{10}{3}\sqrt{3}\)

\(=2\sqrt{3}-10\sqrt{3}-\sqrt{3}-\frac{10}{3}\sqrt{3}\)

\(=-9\sqrt{3}+\frac{10}{3}\sqrt{3}=\left(-9+\frac{10}{3}\right)\sqrt{3}\)

\(=-\frac{17}{3}\sqrt{3}\)

\(\sqrt{150}+\sqrt{1,6}.\sqrt{60}+4,5.\sqrt{2\frac{2}{3}}-\sqrt{6}\)

\(=\sqrt{25.6}+\sqrt{1,6.60}+4,8\sqrt{\frac{8}{3}}-\sqrt{6}\)

\(=5\sqrt{6}+\sqrt{16.6}+4,5.\frac{1}{3}\sqrt{3^2.\frac{4.2}{3}}-\sqrt{6}\)

\(=9\sqrt{6}+3\sqrt{6}-\sqrt{6}=11\sqrt{6}\)

1) Ta có: \(\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

\(=\frac{\sqrt{2}+\sqrt{3}+2+2+\sqrt{6}+\sqrt{8}}{\sqrt{2}+\sqrt{3}+2}\)

\(=\frac{\left(\sqrt{2}+\sqrt{3}+2\right)+\sqrt{2}\left(\sqrt{2}+\sqrt{3}+2\right)}{\left(\sqrt{2}+\sqrt{3}+2\right)}\)

\(=\frac{\left(\sqrt{2}+\sqrt{3}+2\right)\left(1+\sqrt{2}\right)}{\left(\sqrt{2}+\sqrt{3}+2\right)}\)

\(=1+\sqrt{2}\)

2) Ta có: \(2\sqrt{27}-6\sqrt{\frac{4}{3}}+\frac{3}{5}\sqrt{75}\)

\(=\sqrt{108}-\sqrt{36\cdot\frac{4}{3}}+\sqrt{75\cdot\frac{9}{25}}\)

\(=\sqrt{108}-\sqrt{48}+\sqrt{27}\)

\(=\sqrt{3}\left(6-4+3\right)\)

\(=5\sqrt{3}\)

3) Sửa đề: \(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{192}\)

Ta có: \(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{192}\)

\(=\sqrt{2}\cdot\sqrt{4}\cdot\sqrt{3}-10\sqrt{4}\cdot\sqrt{3}+16\cdot\sqrt{4}\cdot\sqrt{3}\)

\(=\sqrt{2}\cdot\sqrt{12}-10\sqrt{12}+16\sqrt{12}\)

\(=\sqrt{12}\left(\sqrt{2}-10+16\right)\)

\(=2\sqrt{3}\left(\sqrt{2}-6\right)\)

\(=2\sqrt{6}-12\sqrt{3}\)

4) Ta có: \(\frac{1}{2+\sqrt{3}}+\frac{\sqrt{2}}{\sqrt{6}}-\frac{2}{3+\sqrt{3}}\)

\(=\frac{2-\sqrt{3}}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}+\frac{\sqrt{12}}{6}-\frac{2\left(3-\sqrt{3}\right)}{\left(3+\sqrt{3}\right)\left(3-\sqrt{3}\right)}\)

\(=\frac{6\left(2-\sqrt{3}\right)+2\sqrt{3}-6+2\sqrt{3}}{6}\)

\(=\frac{12-6\sqrt{3}+2\sqrt{3}-6+2\sqrt{3}}{6}\)

\(=\frac{6-2\sqrt{3}}{6}\)

\(=\frac{2\sqrt{3}\left(\sqrt{3}-1\right)}{2\sqrt{3}\cdot\sqrt{3}}\)

\(=\frac{\sqrt{3}-1}{\sqrt{3}}\)

5) Ta có: \(\left(\sqrt{12}+\sqrt{75}+\sqrt{27}\right):\sqrt{15}\)

\(=\frac{\sqrt{3}\left(2+5+3\right)}{\sqrt{15}}=\frac{10}{\sqrt{5}}=2\sqrt{5}\)

6) Ta có: \(\frac{1}{2}\sqrt{48}-2\sqrt{75}-\frac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\frac{1}{3}}\)

\(=\sqrt{48\cdot\frac{1}{4}}-\sqrt{75\cdot4}-\sqrt{3}+5\sqrt{\frac{4}{3}}\)

\(=\sqrt{12}-\sqrt{300}-\sqrt{3}+\sqrt{25\cdot\frac{4}{3}}\)

\(=\sqrt{12}-\sqrt{300}-\sqrt{3}+\sqrt{\frac{100}{3}}\)

\(=\sqrt{3}\left(2-10-1+\frac{10}{3}\right)\)

\(=-\frac{17\sqrt{3}}{3}=-\frac{17}{\sqrt{3}}\)

Ghi rõ đề ra đi bn

Đề là Tính ă bạn

1.  \(\frac{1}{2}\sqrt{48}-2\sqrt{75}-\frac{\sqrt{33}}{\sqrt{11}}+\sqrt{84}\)= -6,423305878

2. \(\sqrt{150}+\sqrt{1,6}\sqrt{60}+4,5\sqrt{2\frac{2}{3}}-\sqrt{6}\)= 24,79207036

NHA  Vũ Hoàng Thiên An ! ! !

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