Câu 1: Rút gọn các biểu thức sau: A= (\(\sqrt{48}\) - 2\(\sqrt{3}\) + 2\(\sqrt{5}\) )\(\sqrt{5}\) - 2\(\sqrt{45}\)-\(\sqrt{3}\)B= (\(\dfrac{1}{\sqrt{5}-\sqrt{2}}\)\(-\dfrac{1}{\sqrt{5}+\sqrt{2}}\)).\(\dfrac{1}{\left(\sqrt{2}+1\right)^2}\)C= \(2\sqrt{a}\)-\(\sqrt{9a^3}\) a\(^2\) \(\sqrt{\dfrac{4}{a}}\)+ \(\dfrac{2}{a^2}\)\(\sqrt{25a^3}\) với a >...
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Câu 1: Rút gọn các biểu thức sau:
A= (\(\sqrt{48}\) - 2\(\sqrt{3}\) + 2\(\sqrt{5}\) )\(\sqrt{5}\) - 2\(\sqrt{45}\)-\(\sqrt{3}\)
B= (\(\dfrac{1}{\sqrt{5}-\sqrt{2}}\)\(-\dfrac{1}{\sqrt{5}+\sqrt{2}}\)).\(\dfrac{1}{\left(\sqrt{2}+1\right)^2}\)
C= \(2\sqrt{a}\)-\(\sqrt{9a^3}\) a\(^2\) \(\sqrt{\dfrac{4}{a}}\)+ \(\dfrac{2}{a^2}\)\(\sqrt{25a^3}\) với a > 0
a: Ta có: \(A=\left(\sqrt{48}-2\sqrt{3}+2\sqrt{5}\right)\cdot\sqrt{5}-2\sqrt{45}-\sqrt{3}\)
\(=\left(2\sqrt{3}+2\sqrt{5}\right)\cdot\sqrt{5}-6\sqrt{5}-\sqrt{3}\)
\(=2\sqrt{15}+10-6\sqrt{5}-\sqrt{3}\)
b: Ta có: \(B=\left(\dfrac{1}{\sqrt{5}-\sqrt{2}}-\dfrac{1}{\sqrt{5}+\sqrt{2}}\right)\cdot\dfrac{1}{\left(\sqrt{2}+1\right)^2}\)
\(=\dfrac{\sqrt{5}+\sqrt{2}-\sqrt{5}+\sqrt{2}}{3}\cdot\dfrac{1}{3+2\sqrt{2}}\)
\(=\dfrac{2\sqrt{2}}{9+6\sqrt{2}}=\dfrac{-8+6\sqrt{2}}{3}\)