《2025年七彩假日快乐假期暑假作业八年级理综》

1. (★☆☆☆☆)下列计算正确的是(C)
A.$\sqrt {3}+\sqrt {2}= \sqrt {5}$
B.$\sqrt {3}×\sqrt {2}= 6$
C.$\sqrt {12}-\sqrt {3}= \sqrt {3}$
D.$\sqrt {8}÷\sqrt {2}= 4$

答案： C

2. (★☆☆☆☆)计算$\sqrt {8}×\sqrt {\frac {1}{2}}+(\sqrt {2})^{0}$的结果为(C)
A.$2+\sqrt {2}$
B.$\sqrt {2}+1$
C.3
D.5

答案： C

3. (★☆☆☆☆)计算$3÷(-\sqrt {3})÷(-\sqrt {3})$的结果为(C)
A.3
B.9
C.1
D.$3\sqrt {3}$

答案： C

4. (★☆☆☆☆)计算:$\sqrt {8}-\sqrt {2}=$$\sqrt{2}$.

答案： $\sqrt{2}$

5. (★☆☆☆☆)计算$2\sqrt {\frac {1}{2}}-6\sqrt {\frac {1}{3}}+\sqrt {8}$的结果是$3\sqrt{2}-2\sqrt{3}$.

答案： $3\sqrt{2}-2\sqrt{3}$

6. (★★☆☆☆)一个长方体,长、宽、高分别为$\sqrt {\frac {a}{2}},\sqrt {3a^{3}b},\sqrt {8ab}$,它的体积是$2a^{2}b\sqrt{3a}$.

答案： $2a^{2}b\sqrt{3a}$

7. (★★☆☆☆)计算:
(1)$2\sqrt {18}+\sqrt {32}$; (2)$\sqrt {27}-\sqrt {12}+\sqrt {\frac {4}{3}}$;
(3)$\frac {2}{3}\sqrt {9x}+6\sqrt {\frac {x}{4}}$; (4)$2(\sqrt {2}+\sqrt {3})-3(\sqrt {2}-\sqrt {27})$.

答案：
(1) $10\sqrt{2}$
(2) $\frac{5\sqrt{3}}{3}$
(3) $5\sqrt{x}$
(4) $11\sqrt{3}-\sqrt{2}$