Question

Rút gọn căn thức

\(\sqrt{5+5\sqrt{3}}\cdot\sqrt{48-10\sqrt{7+4\sqrt{3}}}\)

Answer 1

 \(=\sqrt{5.\left(\sqrt{3}+1\right)}.\sqrt{48-10\sqrt{\left(2+\sqrt{3}\right)^2}}\)

\(=\sqrt{5}.\left(\sqrt{3}+1\right).\sqrt{48-10.\left(2+\sqrt{3}\right)}\)

\(=\left(\sqrt{15}+\sqrt{5}\right).\sqrt{28-10\sqrt{3}}\)

\(=\left(\sqrt{15}+\sqrt{5}\right).\sqrt{\left(5-\sqrt{3}\right)^2}\)

\(=\left(\sqrt{15}+\sqrt{5}\right).\left(5-\sqrt{3}\right)\)

Vậy...

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