Question

Answer 1

a: \(2\sqrt{32}-3\sqrt{98}-6\sqrt{200}\)

\(=2\cdot4\sqrt{2}-3\cdot7\sqrt{2}-6\cdot10\sqrt{2}\)

\(=8\sqrt{2}-21\sqrt{2}-60\sqrt{2}\)

\(=-73\sqrt{2}\)

b: \(\dfrac{9}{\sqrt{10}-1}+\dfrac{5\sqrt{2}-\sqrt{5}}{\sqrt{5}}+\sqrt{11-2\sqrt{10}}\)

\(=\dfrac{9\left(\sqrt{10}+1\right)}{9}+\dfrac{\sqrt{5}\left(\sqrt{10}-1\right)}{\sqrt{5}}+\sqrt{\left(\sqrt{10}-1\right)^2}\)

\(=\sqrt{10}+1+\sqrt{10}-1+\sqrt{10}-1\)

\(=3\sqrt{10}-1\)