Question

giải giúp a b

Answer 1

a) Ta có: \(\sqrt{3+\sqrt{5}}+\sqrt{3-\sqrt{5}}\)

\(=\dfrac{\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{5}+1+\sqrt{5}-1}{\sqrt{2}}=\dfrac{2\sqrt{5}}{\sqrt{2}}=\sqrt{10}\)

b) Ta có: \(2\sqrt{2}\left(\sqrt{3}-2\right)+\left(9+4\sqrt{2}\right)\)

\(=2\sqrt{6}-4\sqrt{2}+9+4\sqrt{2}\)

\(=9+2\sqrt{6}\)

c) Ta có: \(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\left(2+\sqrt{3}\right)}}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{28-10\sqrt{3}}}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+5\left(5-\sqrt{3}\right)}}\)

\(=\sqrt{4+\sqrt{25}}=\sqrt{4+5}=3\)(đpcm)