Question

Rút gọn \(\sqrt{75}-3\sqrt{27}-6\sqrt{\frac{1}{3}}+2\sqrt{\frac{4}{3}}\)

Answer 1

\(\sqrt{75}-3\sqrt{27}-6\sqrt{\frac{1}{3}}+2\sqrt{\frac{4}{3}}\)

=\(\sqrt{25}\sqrt{3}-3\sqrt{9}\sqrt{3}-6\sqrt{\frac{1}{3}}+2\sqrt{4}\sqrt{\frac{1}{3}}\)

=\(5\sqrt{3}-9\sqrt{3}-6\sqrt{\frac{1}{3}}+4\sqrt{\frac{1}{3}}\)

=\(-4\sqrt{3}-2\sqrt{\frac{1}{3}}\)

=\(-4\sqrt{3}-\frac{2}{\sqrt{3}}\)

=\(-4\sqrt{3}-\frac{2\sqrt{3}}{3}\)

=\(\frac{-12\sqrt{3}}{3}-\frac{2\sqrt{3}}{3}=\frac{-14\sqrt{3}}{3}\)

Answer 2

\(\sqrt{75}-3\sqrt{27}-6\sqrt{\frac{1}{3}}+2\sqrt{\frac{4}{3}}=\sqrt{3.25}-9\sqrt{3}-2\sqrt{3}+\frac{4\sqrt{3}}{3}=-4\sqrt{3}-2\sqrt{3}+\frac{4\sqrt{3}}{3}=-6\sqrt{3}+\frac{4\sqrt{3}}{3}=-\sqrt{\frac{14\sqrt{3}}{3}}\)