Question

\(\sqrt{\frac{2}{3}}+2\sqrt{\frac{3}{2}}-\sqrt{6}\)

\(3\sqrt{\frac{2}{5}}+\sqrt{\frac{5}{2}}-2\sqrt{10}\)

\(\sqrt{\frac{3a}{7}}-2\sqrt{\frac{7a}{3}}+\sqrt{21a}\)

Answer 1

a, \(=\sqrt{\frac{2}{3}}+\sqrt{\frac{2^2.3}{2}}-\sqrt{6}\)

\(=\sqrt{\frac{2}{3}}+\sqrt{6}-\sqrt{6}=\sqrt{\frac{2}{3}}=\frac{\sqrt{6}}{3}\)

b, \(=\frac{3\sqrt{10}}{5}+\frac{\sqrt{10}}{2}-2\sqrt{10}=\frac{3\sqrt{10}}{5}-\frac{3\sqrt{10}}{2}\)

\(=3\sqrt{10}\left(\frac{1}{5}-\frac{1}{2}\right)=-\frac{6\sqrt{10}}{10}\)

c, \(=\frac{\sqrt{21a}}{7}-\frac{2\sqrt{21a}}{3}+\sqrt{21a}\)

\(=\sqrt{21a}\left(\frac{1}{7}-\frac{2}{3}+1\right)=\frac{10\sqrt{21a}}{21}\)