Question

9) \(\sqrt{20}\) + 2\(\sqrt{45}\) + \(\sqrt{125}\) - 3\(\sqrt{80}\)

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

Answer 1

9.

\(\sqrt{20}+2\sqrt{45}+\sqrt{125}-3\sqrt{80}\)

\(=2\sqrt{5}+6\sqrt{5}+5\sqrt{5}-12\sqrt{5}\)

\(=-\sqrt{5}\)

Answer 2

10.

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

\(=5\sqrt{3}-\sqrt{5+\dfrac{1}{3}}+\dfrac{9}{2}\sqrt{2+\dfrac{2}{3}}+6\sqrt{3}\)

\(=11\sqrt{3}-\sqrt{\dfrac{16}{3}}+\dfrac{9}{2}\sqrt{\dfrac{8}{3}}\)

\(=11\sqrt{3}-\dfrac{4\sqrt{3}}{3}+3\sqrt{6}\)

\(=\dfrac{29\sqrt{3}}{3}+3\sqrt{6}\)

Answer 3

\(\sqrt{20}+2\sqrt{45}+\sqrt{125}-3\sqrt{80}\\ =2\sqrt{5}+6\sqrt{5}+5\sqrt{5}-12\sqrt{5}=\sqrt{5}\)

\(\sqrt{75}-\sqrt{5\dfrac{1}{3}}+\dfrac{9}{2}\sqrt{2\dfrac{2}{3}}+2\sqrt{27}\\ =5\sqrt{3}-\dfrac{4\sqrt{3}}{3}+3\sqrt{6}+6\sqrt{3}\\ =\dfrac{15\sqrt{3}-4\sqrt{3}+6\sqrt{6}+18\sqrt{3}}{3}\\ =\dfrac{29\sqrt{3}+6\sqrt{6}}{3}\)

Answer 4

\(9,=2\sqrt{5}+6\sqrt{5}+5\sqrt{5}-12\sqrt{5}=\sqrt{5}\)

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Answer 5

9: Ta có: \(\sqrt{20}+2\sqrt{45}+\sqrt{125}-3\sqrt{80}\)

\(=2\sqrt{5}+6\sqrt{5}+5\sqrt{5}-12\sqrt{5}\)

\(=\sqrt{5}\)

10: Ta có: \(\sqrt{75}-\sqrt{5\dfrac{1}{3}}+\dfrac{9}{2}\cdot\sqrt{2\dfrac{2}{3}}+2\sqrt{27}\)

\(=5\sqrt{3}+6\sqrt{3}-\dfrac{4}{3}\sqrt{3}+3\sqrt{6}\)

\(=\dfrac{29}{3}\sqrt{3}+3\sqrt{6}\)