Question

[Đặng Lâm Oanh]

Tính giá trị biểu thức

Answer 1

[Hoàng Như Quỳnh]

\(1,\sqrt{2}\left(3-2\sqrt{9}+2\sqrt{16}-\sqrt{25}\right)=\sqrt{2}\left(3-6+8-5\right)\)

\(=\sqrt{2}.0=0\)

\(2,\sqrt{2}\left(\sqrt{25}-\sqrt{9}+\sqrt{100}-\sqrt{81}\right)\)

\(=\sqrt{2}\left(5-3+10-9\right)=3\sqrt{2}\)

\(3,\sqrt{5}\left(5+\sqrt{4}-3\sqrt{9}\right)=\sqrt{5}\left(5+2-9\right)=-2\sqrt{5}\)

\(4,\sqrt{3}\left(5\sqrt{16}-4\sqrt{9}-2\sqrt{25}+\sqrt{36}\right)\)

\(=\sqrt{3}\left(20-12-10+6\right)=4\sqrt{3}\)

\(5,\sqrt{12}-\sqrt{300}-\sqrt{3}+\frac{10\sqrt{3}}{3}\)

\(\sqrt{3}\left(\sqrt{4}-\sqrt{100}-1+\frac{10}{3}\right)=\sqrt{3}\left(2-10-1+\frac{10}{3}\right)=-\frac{17\sqrt{3}}{3}\)

\(6,\sqrt{3}\left(3\sqrt{4}-4\sqrt{9}+5\sqrt{16}\right)=\sqrt{3}\left(6-12+20\right)\)

\(=14\sqrt{3}\)

\(7,\sqrt{3}\left(2+5-4\right)=3\sqrt{3}\)

\(8,\sqrt{2}\left(8+8-15\right)=\sqrt{2}\)

\(9,\sqrt{5}\left(6-6+4\right)=4\sqrt{5}\)

\(10,\sqrt{6}\left(3-6+3-5\right)=-5\sqrt{6}\)

Answer 2

[Phạm Nguyễn Hà Chi]

11, \(2\sqrt{18}-7\sqrt{2}+\sqrt{162}\)

\(=2.3\sqrt{2}-7\sqrt{2}+9\sqrt{2}\)

\(=6\sqrt{2}-7\sqrt{2}+9\sqrt{2}\)

\(=8\sqrt{2}\)

12, \(3\sqrt{8}-4\sqrt{18}+5\sqrt{32}-\sqrt{50}\)

\(=3.2\sqrt{2}-4.3\sqrt{2}+5.4\sqrt{2}-5\sqrt{2}\)

\(=6\sqrt{2}-12\sqrt{2}+20\sqrt{2}-5\sqrt{2}\)

\(=9\sqrt{2}\)

13, \(\sqrt{125}-2\sqrt{20}-3\sqrt{80}+4\sqrt{45}\)

\(=5\sqrt{5}-2.2\sqrt{5}-3.4\sqrt{5}+4.3\sqrt{5}\)

\(=5\sqrt{5}-4\sqrt{5}-12\sqrt{5}+12\sqrt{5}\)

\(=\sqrt{5}\)

14, \(2\sqrt{28}+2\sqrt{63}-3\sqrt{175}+\sqrt{112}\)

\(=2.2\sqrt{7}+2.3\sqrt{7}-3.5\sqrt{7}+4\sqrt{7}\)

\(=4\sqrt{7}+6\sqrt{7}-15\sqrt{7}+4\sqrt{7}\)

\(=-\sqrt{7}\)

15, \(3\sqrt{2}+\sqrt{8}+\frac{1}{2}\sqrt{50}-\sqrt{32}\)

\(=3\sqrt{2}+2\sqrt{2}+\frac{1}{2}.5\sqrt{2}-4\sqrt{2}\)

\(=3\sqrt{2}+2\sqrt{2}+\frac{5}{2}\sqrt{2}-4\sqrt{2}\)

\(=\frac{7}{2}\sqrt{2}\)

16, \(3\sqrt{50}-2\sqrt{12}-\sqrt{18}+\sqrt{75}-\sqrt{8}\)

\(=3.5\sqrt{2}-2.2\sqrt{3}-3\sqrt{2}+5\sqrt{3}-2\sqrt{2}\)

\(=15\sqrt{2}-4\sqrt{3}-3\sqrt{2}+5\sqrt{3}-2\sqrt{2}\)

\(=10\sqrt{2}+\sqrt{3}\)

17, \(2\sqrt{75}-3\sqrt{12}+\sqrt{27}\)

\(=2.5\sqrt{3}-3.2\sqrt{3}+3\sqrt{3}\)

\(=10\sqrt{3}-6\sqrt{3}+3\sqrt{3}\)

\(=7\sqrt{3}\)

18, \(\sqrt{12}+\sqrt{75}-\sqrt{27}\)

\(=2\sqrt{3}+5\sqrt{3}-3\sqrt{3}\)

\(=4\sqrt{3}\)

19, \(\sqrt{27}-\sqrt{12}+\sqrt{75}+\sqrt{147}\)

\(=3\sqrt{3}-2\sqrt{3}+5\sqrt{3}+7\sqrt{3}\)

\(=13\sqrt{3}\)

20, \(2\sqrt{3}+\sqrt{48}-\sqrt{75}-\sqrt{243}\)

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

\(=-8\sqrt{3}\)

21, \(6\sqrt{\frac{8}{9}}-5\sqrt{\frac{32}{25}}+14\sqrt{\frac{18}{49}}\)

\(=6.\frac{2\sqrt{2}}{3}-5.\frac{4\sqrt{2}}{5}+14.\frac{3\sqrt{2}}{7}\)

\(=4\sqrt{2}-4\sqrt{2}+6\sqrt{2}\)

\(=6\sqrt{2}\)