Question

Answer 1

a: \(A=10\sqrt{27}-\dfrac{4\sqrt{15}}{\sqrt{5}}-5\sqrt{24}\cdot\sqrt{2}\)

\(=10\cdot3\sqrt{3}-4\sqrt{3}-5\sqrt{48}\)

\(=30\sqrt{3}-4\sqrt{3}-5\cdot4\sqrt{3}\)

\(=26\sqrt{3}-20\sqrt{3}=6\sqrt{3}\)

b: \(B=\dfrac{\sqrt{12}-\sqrt{16}}{\sqrt{3}-2}+\dfrac{\sqrt{21}+\sqrt{7}}{\sqrt{3}+1}+\sqrt{\left(2-\sqrt{7}\right)^2}\)

\(=\dfrac{2\sqrt{3}-4}{\sqrt{3}-2}+\dfrac{\sqrt{7}\left(\sqrt{3}+1\right)}{\sqrt{3}+1}+\left|2-\sqrt{7}\right|\)

\(=2+\sqrt{7}+\sqrt{7}-2=2\sqrt{7}\)