Question

Answer 1

d) \(\sqrt{75}-\sqrt{5\dfrac{1}{3}}+\dfrac{9}{2}\sqrt{2\dfrac{2}{3}}+2\sqrt{27}\)

  \(=5\sqrt{3}-\dfrac{4}{\sqrt{3}}+\dfrac{9}{2}\cdot\dfrac{2\sqrt{2}}{\sqrt{3}}+2\cdot3\sqrt{3}\)

 \(=11\sqrt{3}-\dfrac{1}{\sqrt{3}}\cdot\left(4-9\sqrt{2}\right)\)

 \(=\dfrac{11\cdot3-4+9\sqrt{2}}{\sqrt{3}}=\dfrac{29+9\sqrt{2}}{\sqrt{3}}=\dfrac{29\sqrt{3}+9\sqrt{6}}{\sqrt{3}}\)