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a) Ta có: \(A=\sqrt{20}-2\sqrt{45}+3\sqrt{18}+\sqrt{72}\)
\(=2\sqrt{5}-6\sqrt{5}+9\sqrt{2}+6\sqrt{2}\)
\(=-4\sqrt{5}+15\sqrt{2}\)
b) Ta có: \(B=4\sqrt{\left(\sqrt{3}-1\right)^2}+2\sqrt{12}+4\sqrt{\dfrac{1}{2}}\)
\(=4\left(\sqrt{3}-1\right)+2\cdot2\sqrt{3}+\dfrac{4}{\sqrt{2}}\)
\(=4\sqrt{3}-4+4\sqrt{3}+2\sqrt{2}\)
\(=8\sqrt{3}+2\sqrt{2}-4\)
c) Ta có: \(C=\left(3+\dfrac{3-\sqrt{3}}{\sqrt{3}-1}\right)\left(3-\dfrac{3+\sqrt{3}}{1+\sqrt{3}}\right)\)
\(=\left(3+\sqrt{3}\right)\left(3-\sqrt{3}\right)\)
=9-3
=6
d) Ta có: \(D=\dfrac{1}{2+\sqrt{3}}+\dfrac{1}{2-\sqrt{3}}\)
\(=2-\sqrt{3}+2+\sqrt{3}\)
=4
\(\sqrt{\dfrac{72x}{128}}=\dfrac{3}{4}\)
\(\Leftrightarrow x\cdot\dfrac{9}{16}=\dfrac{9}{16}\)
hay x=1
a: \(\left(4\sqrt{8}-\sqrt{72}+5\sqrt{\dfrac{1}{2}}\right)\cdot2\sqrt{2}\)
\(=\left(4\cdot2\sqrt{2}-6\sqrt{2}+\dfrac{5}{\sqrt{2}}\right)\cdot2\sqrt{2}\)
\(=\left(2\sqrt{2}+\dfrac{5}{\sqrt{2}}\right)\cdot2\sqrt{2}\)
\(=2\sqrt{2}\cdot2\sqrt{2}+\dfrac{5}{\sqrt{2}}\cdot2\sqrt{2}\)
\(=8+10=18\)
b: Sửa đề:\(\dfrac{5+\sqrt{5}}{\sqrt{5}}+\dfrac{3+\sqrt{3}}{\sqrt{3}+1}-\left(\sqrt{3}+\sqrt{5}\right)\)
\(=\dfrac{\sqrt{5}\left(\sqrt{5}+1\right)}{\sqrt{5}}+\dfrac{\sqrt{3}\left(\sqrt{3}+1\right)}{\sqrt{3}+1}-\left(\sqrt{3}+\sqrt{5}\right)\)
\(=\sqrt{5}+1+\sqrt{3}-\sqrt{3}-\sqrt{5}\)
=1
\(\left(4\sqrt{8}-\sqrt{72}+5\sqrt{\dfrac{1}{2}}\right)2\sqrt{2}\\ =\left(8\sqrt{2}-6\sqrt{2}+5\sqrt{\dfrac{1}{2}}\right)2\sqrt{2}\\ =8.2.\sqrt{2}.\sqrt{2}-6.2.\sqrt{2}.\sqrt{2}+5.2.\sqrt{2}.\sqrt{\dfrac{1}{2}}\\ =32-24+10\\ =18\\ \dfrac{5+\sqrt{5}}{\sqrt{5}}+\dfrac{3+\sqrt{3}}{\sqrt{3}+1}\left(\sqrt{3}+\sqrt{5}\right)\\ =\dfrac{\sqrt{5}\left(\sqrt{5}+1\right)}{\sqrt{5}}+\dfrac{\sqrt{3}\left(\sqrt{3}+1\right)}{\sqrt{3}}\left(\sqrt{3}+\sqrt{5}\right)\\ =\sqrt{5}+1+\sqrt{3}\left(\sqrt{3}+\sqrt{5}\right)\\ =\sqrt{5}+1+3+\sqrt{15}\\ =4+\sqrt{5}+\sqrt{15}\)
c: Ta có: \(C=\left(\dfrac{\sqrt{3}+1}{\sqrt{3}-1}-\dfrac{\sqrt{3}-1}{\sqrt{3}+1}\right):\sqrt{48}\)
\(=\dfrac{4+2\sqrt{3}-4+2\sqrt{3}}{2}:4\sqrt{3}\)
\(=\dfrac{1}{2}\)
6: Ta có: \(\left(3\sqrt{2}-\sqrt{3}\right)\left(3\sqrt{2}+\sqrt{3}\right)\)
=18-3
=15
7: Ta có: \(\sqrt{72}+\sqrt{4\dfrac{1}{2}}-\sqrt{32}-\sqrt{162}\)
\(=6\sqrt{2}+\dfrac{3}{2}\sqrt{2}-4\sqrt{2}-9\sqrt{2}\)
\(=-\dfrac{11}{2}\sqrt{2}\)
a: \(A=\left(1-\sqrt{7}\right)\cdot\left(1+\sqrt{7}\right)=1-7=-6\)
b: \(B=3\sqrt{3}+8\sqrt{3}-15\sqrt{3}=-4\sqrt{3}\)
c: \(C=4\sqrt{2}-5\sqrt{2}+3\sqrt{2}=2\sqrt{2}\)
\(A=\dfrac{\sqrt[4]{7\sqrt[3]{54}+15\sqrt[3]{128}}}{\sqrt[3]{\sqrt[4]{32}}+\sqrt[3]{9\sqrt[4]{162}}}\)
\(\Leftrightarrow A=\dfrac{\sqrt[4]{7\sqrt[3]{3^3.2}+15\sqrt[3]{4^3.2}}}{\sqrt[3]{\sqrt[4]{2^4.2}}+\sqrt[3]{9\sqrt[4]{3^4.2}}}\)
\(\Leftrightarrow A=\dfrac{\sqrt[4]{7.3\sqrt[3]{2}+15.4\sqrt[3]{2}}}{\sqrt[3]{2\sqrt[4]{2}}+\sqrt[3]{9.3\sqrt[4]{2}}}\)
\(\Leftrightarrow A=\dfrac{\sqrt[4]{21\sqrt[3]{2}+60\sqrt[3]{2}}}{\sqrt[3]{2\sqrt[4]{2}}+\sqrt[3]{3^3\sqrt[4]{2}}}\)
\(\Leftrightarrow A=\dfrac{\sqrt[4]{81\sqrt[3]{2}}}{\sqrt[3]{\sqrt[4]{2}}\left(\sqrt[3]{2}+3\right)}=\dfrac{3\sqrt[4]{\sqrt[3]{2}}}{\sqrt[3]{\sqrt[4]{2}}\left(\sqrt[3]{2}+3\right)}\)
\(\Leftrightarrow A=\dfrac{3}{\sqrt[3]{2}+3}\)
a. ĐKXĐ: $x\geq 1$
PT $\Leftrightarrow \frac{1}{2}\sqrt{x-1}-\frac{3}{2}.\sqrt{9}.\sqrt{x-1}+24.\sqrt{\frac{1}{64}}.\sqrt{x-1}=-17$
$\Leftrightarrow \frac{1}{2}\sqrt{x-1}-\frac{9}{2}\sqrt{x-1}+3\sqrt{x-1}=-17$
$\Leftrightarrow -\sqrt{x-1}=-17$
$\Leftrightarrow \sqrt{x-1}=17$
$\Leftrightarrow x-1=289$
$\Leftrightarrow x=290$
b. ĐKXĐ: $x\geq \frac{1}{2}$
PT $\Leftrightarrow \sqrt{9}.\sqrt{2x-1}-0,5\sqrt{2x-1}+\frac{1}{2}.\sqrt{25}.\sqrt{2x-1}+\sqrt{49}.\sqrt{2x-1}=24$
$\Leftrightarrow 3\sqrt{2x-1}-0,5\sqrt{2x-1}+2,5\sqrt{2x-1}+7\sqrt{2x-1}=24$
$\Leftrightarrow 12\sqrt{2x-1}=24$
$\Leftrihgtarrow \sqrt{2x-1}=2$
$\Leftrightarrow x=2,5$ (tm)
c. ĐKXĐ: $x\geq 2$
PT $\Leftrightarrow \sqrt{36}.\sqrt{x-2}-15\sqrt{\frac{1}{25}}\sqrt{x-2}=4(5+\sqrt{x-2})$
$\Leftrightarrow 6\sqrt{x-2}-3\sqrt{x-2}=20+4\sqrt{x-2}$
$\Leftrightarrow \sqrt{x-2}=-20< 0$ (vô lý)
Vậy pt vô nghiệm
\(\left(\sqrt[3]{\dfrac{1}{9}}+4\cdot\sqrt[3]{\dfrac{1}{72}}-\sqrt[3]{4}\right)\left(\sqrt[3]{72}+\sqrt[3]{96}+\sqrt[3]{128}\right)\)
\(=\left(\dfrac{1}{3}\cdot\sqrt[3]{3}+4\cdot\dfrac{1}{6}\cdot\sqrt[3]{3}-2\sqrt[3]{\dfrac{1}{2}}\right)\left(2\sqrt[3]{9}+2\sqrt[3]{12}+4\sqrt[3]{2}\right)\)
\(=\left(\sqrt[3]{3}-2\sqrt[3]{\dfrac{1}{2}}\right)\left(6\sqrt[3]{3}+2\sqrt[3]{12}+4\sqrt[3]{2}\right)\)
\(=6\cdot3+2\sqrt[3]{36}+4\sqrt[3]{6}-12\sqrt[3]{\dfrac{3}{2}}-4\sqrt[3]{6}-8\)
\(=10+12\sqrt[3]{\dfrac{1}{6}}-6\sqrt[3]{12}\)