1. (2024·秦淮区期末)下列二次根式中,最简二次根式是()

A.$\sqrt{1.2}$
B.$\sqrt{14}$
C.$\sqrt{18}$
D.$\sqrt{\frac{1}{2}}$

B

2. 将$\sqrt{\frac{45}{2}}$化为最简二次根式,其结果是()

A.$\frac{\sqrt{45}}{2}$
B.$\frac{\sqrt{90}}{2}$
C.$\frac{9\sqrt{10}}{2}$
D.$\frac{3\sqrt{10}}{2}$

D

3. 下列各式中,化简正确的是()

A.$\sqrt{\frac{5}{3}} = 3\sqrt{15}$
B.$\sqrt{\frac{1}{2}} = \pm \frac{1}{2}\sqrt{2}$
C.$\sqrt{a^{4}b} = a^{2}\sqrt{b}$
D.$\sqrt{x^{3}-x^{2}} = -x\sqrt{x - 1}$

C

4. 计算$\sqrt{3}×\sqrt{2}÷\frac{1}{\sqrt{6}}$的结果为.

6

5. 把下列各式化成最简二次根式:
(1)$\sqrt{\frac{49a^{3}}{9}}$;
(2)$\sqrt{\frac{1}{4}+\frac{1}{9}}$;
(3)$x^{2}\sqrt{\frac{2}{x}}$.

解：原式$​=\frac {7}{3}a\sqrt {a}​$
解：原式$​=\sqrt {\frac {13}{36}}​$
$​=\frac {\sqrt {13}}{6}​$
解：原式$​=x·\sqrt {x²·\frac {2}{x}}​$
$​= x\sqrt {2x}​$

6. 计算:
(1)$\sqrt{18}÷\sqrt{\frac{27}{2}}$;
(2)$\sqrt{6x^{2}}÷\sqrt{12x^{3}y}(y ＞ 0)$;
(3)$-6\sqrt{8}×2\sqrt{6}÷4\sqrt{27}$;
(4)$\sqrt{30}÷3\sqrt{\frac{8}{5}}×\frac{2}{3}\sqrt{\frac{20}{3}}$.

解：原式$​=\sqrt {18÷\frac {27}{2}}​$
$​=\sqrt {18×\frac {2}{27}}​$
$​=\sqrt {\frac {12}{9}}​$
$​=\frac {2\sqrt {3}}{3}​$
解：原式$​=\sqrt {\frac {6x^2}{12x^3y}}​$
$​=\sqrt {\frac {1}{2xy}}​$
$​=\frac {\sqrt {2xy}}{2xy}​$
解：原式$​=-12\sqrt {2}×2\sqrt {6}÷12\sqrt {3}​$
$​=-48\sqrt {3}÷12\sqrt {3}​$
​=-4​
解：原式$​=(1×\frac {1}{3}×\frac {2}{3})×\sqrt {30×\frac {5}{8}×\frac {20}{3}}​$
$​=\frac {2}{9}×5\sqrt {5}​$
$​=\frac {10}{9}\sqrt {5}​$