2. 有下列等式:①$\sqrt{3}+\sqrt{2}=\sqrt{5}$;②$2+\sqrt{3}=2\sqrt{3}=2$;③$\sqrt{5}+\sqrt{\frac{1}{5}}=\sqrt{5}+\frac{1}{5}\sqrt{5}=\frac{6}{5}\sqrt{5}$;④$\sqrt{3^{2}+4^{2}}=3 + 4 = 7$.其中,正确的有 ( )
A. 1个
B. 2个
C. 3个
D. 0个
A. 1个
B. 2个
C. 3个
D. 0个
答案
A
3. 与$\sqrt{\frac{1}{8}}$是同类二次根式的是 ( )
A. $\sqrt{12}$
B. $\sqrt{18}$
C. $\sqrt{\frac{1}{4}}$
D. $\sqrt{0.8}$
A. $\sqrt{12}$
B. $\sqrt{18}$
C. $\sqrt{\frac{1}{4}}$
D. $\sqrt{0.8}$
答案
B
4. 下列等式成立的是 ( )
A. $\sqrt{a}+\sqrt{b}=\sqrt{a + b}$
B. $3\sqrt{a}-1=2\sqrt{a}$
C. $\frac{\sqrt{8}+\sqrt{18}}{2}=\sqrt{4}+\sqrt{9}=2 + 3 = 5$
D. $\sqrt{3\frac{3}{8}}=3\sqrt{\frac{3}{8}}$
A. $\sqrt{a}+\sqrt{b}=\sqrt{a + b}$
B. $3\sqrt{a}-1=2\sqrt{a}$
C. $\frac{\sqrt{8}+\sqrt{18}}{2}=\sqrt{4}+\sqrt{9}=2 + 3 = 5$
D. $\sqrt{3\frac{3}{8}}=3\sqrt{\frac{3}{8}}$
答案
D
5. 化简下列各组二次根式,看看它们是不是同类二次根式:
(1)$2\sqrt{12}$与$\sqrt{27}$; (2)$\sqrt{50}$与$3\sqrt{8}$; (3)$2\sqrt{1\frac{1}{2}}$与$2\sqrt{48}$.
(1)$2\sqrt{12}$与$\sqrt{27}$; (2)$\sqrt{50}$与$3\sqrt{8}$; (3)$2\sqrt{1\frac{1}{2}}$与$2\sqrt{48}$.
答案
略
6. 计算:
(1)$3\sqrt{5}-\sqrt{2}+\sqrt{5}-4\sqrt{2}$; (2)$5\sqrt{3}-3\sqrt{75}-\sqrt{27}$;
(3)$\sqrt{72}+\sqrt{18}-\frac{3\sqrt{2}}{2}$; (4)$\sqrt{32}-2\sqrt{12}-\sqrt{\frac{1}{3}}-\frac{6}{\sqrt{2}}$;
(5)$2\sqrt{12}-4\sqrt{\frac{1}{27}}+3\sqrt{48}$; (6)$(\sqrt{0.5}-2\sqrt{\frac{1}{3}})-(\sqrt{\frac{1}{8}}-\sqrt{75})$.
(1)$3\sqrt{5}-\sqrt{2}+\sqrt{5}-4\sqrt{2}$; (2)$5\sqrt{3}-3\sqrt{75}-\sqrt{27}$;
(3)$\sqrt{72}+\sqrt{18}-\frac{3\sqrt{2}}{2}$; (4)$\sqrt{32}-2\sqrt{12}-\sqrt{\frac{1}{3}}-\frac{6}{\sqrt{2}}$;
(5)$2\sqrt{12}-4\sqrt{\frac{1}{27}}+3\sqrt{48}$; (6)$(\sqrt{0.5}-2\sqrt{\frac{1}{3}})-(\sqrt{\frac{1}{8}}-\sqrt{75})$.
答案
(1)$4\sqrt{5}-5\sqrt{2}$ (2)$-13\sqrt{3}$ (3)$\frac{15\sqrt{2}}{2}$
(4)$\sqrt{2}-\frac{13\sqrt{3}}{3}$ (5)$\frac{140\sqrt{3}}{9}$ (6)$\frac{\sqrt{2}}{4}+\frac{13\sqrt{3}}{3}$
(4)$\sqrt{2}-\frac{13\sqrt{3}}{3}$ (5)$\frac{140\sqrt{3}}{9}$ (6)$\frac{\sqrt{2}}{4}+\frac{13\sqrt{3}}{3}$
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