1. 计算：
(1)$\sqrt{3}×\sqrt{2}÷\sqrt{30}$； (2)$\sqrt{15}÷\sqrt{30}×\sqrt{1\frac{1}{3}}$；
(3)$\sqrt{12}×\sqrt{27}÷\sqrt{\frac{1}{2}}$； (4)$\sqrt{18}÷\sqrt{\frac{3}{4}}×\sqrt{\frac{4}{3}}$；
(5)$\sqrt{24}÷\frac{\sqrt{2}}{4}÷\sqrt{48}$； (6)$\frac{2}{3}\sqrt{18}÷(-\sqrt{3})×\frac{1}{3}\sqrt{27}$；
(7)$\sqrt{30}×\frac{3}{2}\sqrt{2\frac{2}{3}}×\frac{1}{2}\sqrt{\frac{2}{5}}$； (8)$\sqrt{3\frac{1}{3}}÷(\frac{2}{5}\sqrt{2\frac{1}{3}})×(4\sqrt{1\frac{2}{5}})$.
答案：1. (1) $\frac{\sqrt{5}}{5}$ (2) $\frac{\sqrt{6}}{3}$ (3) $18\sqrt{2}$ (4) $4\sqrt{2}$ (5) $2$ (6) $-2\sqrt{2}$ (7) $3\sqrt{2}$ (8) $10\sqrt{2}$
解析：
(1) $\sqrt{3}×\sqrt{2}÷\sqrt{30}=\sqrt{3×2}÷\sqrt{30}=\sqrt{6}÷\sqrt{30}=\sqrt{\frac{6}{30}}=\sqrt{\frac{1}{5}}=\frac{\sqrt{5}}{5}$
(2) $\sqrt{15}÷\sqrt{30}×\sqrt{1\frac{1}{3}}=\sqrt{\frac{15}{30}}×\sqrt{\frac{4}{3}}=\sqrt{\frac{1}{2}}×\sqrt{\frac{4}{3}}=\sqrt{\frac{1}{2}×\frac{4}{3}}=\sqrt{\frac{2}{3}}=\frac{\sqrt{6}}{3}$
(3) $\sqrt{12}×\sqrt{27}÷\sqrt{\frac{1}{2}}=\sqrt{12×27}÷\sqrt{\frac{1}{2}}=\sqrt{324}×\sqrt{2}=18\sqrt{2}$
(4) $\sqrt{18}÷\sqrt{\frac{3}{4}}×\sqrt{\frac{4}{3}}=\sqrt{18÷\frac{3}{4}×\frac{4}{3}}=\sqrt{18×\frac{4}{3}×\frac{4}{3}}=\sqrt{32}=4\sqrt{2}$
(5) $\sqrt{24}÷\frac{\sqrt{2}}{4}÷\sqrt{48}=\sqrt{24}×\frac{4}{\sqrt{2}}×\frac{1}{\sqrt{48}}=4×\sqrt{\frac{24}{2×48}}=4×\sqrt{\frac{1}{4}}=4×\frac{1}{2}=2$
(6) $\frac{2}{3}\sqrt{18}÷(-\sqrt{3})×\frac{1}{3}\sqrt{27}=\frac{2}{3}×3\sqrt{2}÷(-\sqrt{3})×\frac{1}{3}×3\sqrt{3}=2\sqrt{2}÷(-\sqrt{3})×\sqrt{3}=-2\sqrt{2}$
(7) $\sqrt{30}×\frac{3}{2}\sqrt{2\frac{2}{3}}×\frac{1}{2}\sqrt{\frac{2}{5}}=\frac{3}{2}×\frac{1}{2}×\sqrt{30×\frac{8}{3}×\frac{2}{5}}=\frac{3}{4}×\sqrt{32}=\frac{3}{4}×4\sqrt{2}=3\sqrt{2}$
(8) $\sqrt{3\frac{1}{3}}÷(\frac{2}{5}\sqrt{2\frac{1}{3}})×(4\sqrt{1\frac{2}{5}})=\sqrt{\frac{10}{3}}÷(\frac{2}{5}\sqrt{\frac{7}{3}})×(4\sqrt{\frac{7}{5}})=\frac{5}{2}×4×\sqrt{\frac{10}{3}÷\frac{7}{3}×\frac{7}{5}}=10×\sqrt{2}=10\sqrt{2}$
2. 计算：
(1)$\sqrt{a^{3}}·\sqrt{ab}÷\sqrt{9a^{2}b^{3}}$； (2)$\sqrt{3a^{2}}÷3\sqrt{\frac{a}{2}}·\frac{1}{2}\sqrt{\frac{2a}{3}}$；
(3)$\sqrt{xy^{2}}÷\sqrt{5xy}·\sqrt{15x}$； (4)$\frac{2}{b}\sqrt{ab^{5}}·(-\frac{3}{2}\sqrt{a^{3}b})÷3\sqrt{\frac{b}{a}}(a＞0,b＞0)$.
答案：2. (1) $\frac{a}{3b}$ (2) $\frac{a}{3}$ (3) $\sqrt{3xy}$ (4) $-a^{2}b\sqrt{ab}$
解析：
(1) $\sqrt{a^{3}}·\sqrt{ab}÷\sqrt{9a^{2}b^{3}}$
$=a^{\frac{3}{2}}·(ab)^{\frac{1}{2}}÷(3a b^{\frac{3}{2}})$
$=a^{\frac{3}{2}}·a^{\frac{1}{2}}b^{\frac{1}{2}}÷(3a b^{\frac{3}{2}})$
$=a^{2}b^{\frac{1}{2}}÷(3a b^{\frac{3}{2}})$
$=\frac{1}{3}a b^{-1}$
$=\frac{a}{3b}$
(2) $\sqrt{3a^{2}}÷3\sqrt{\frac{a}{2}}·\frac{1}{2}\sqrt{\frac{2a}{3}}$
$=a\sqrt{3}÷(3×\frac{\sqrt{2a}}{2})·\frac{1}{2}×\frac{\sqrt{6a}}{3}$
$=a\sqrt{3}×\frac{2}{3\sqrt{2a}}·\frac{\sqrt{6a}}{6}$
$=a\sqrt{3}×\frac{2\sqrt{6a}}{3\sqrt{2a}×6}$
$=a\sqrt{3}×\frac{2\sqrt{3}×\sqrt{2a}}{3\sqrt{2a}×6}$
$=a\sqrt{3}×\frac{\sqrt{3}}{9}$
$=a×\frac{3}{9}$
$=\frac{a}{3}$
(3) $\sqrt{xy^{2}}÷\sqrt{5xy}·\sqrt{15x}$
$=y\sqrt{x}÷\sqrt{5xy}·\sqrt{15x}$
$=y\sqrt{x}×\frac{1}{\sqrt{5xy}}×\sqrt{15x}$
$=y\sqrt{x}×\frac{\sqrt{15x}}{\sqrt{5xy}}$
$=y\sqrt{x}×\sqrt{\frac{15x}{5xy}}$
$=y\sqrt{x}×\sqrt{\frac{3}{y}}$
$=y\sqrt{x}×\frac{\sqrt{3y}}{y}$
$=\sqrt{3xy}$
(4) $\frac{2}{b}\sqrt{ab^{5}}·(-\frac{3}{2}\sqrt{a^{3}b})÷3\sqrt{\frac{b}{a}}$
$=\frac{2}{b}×b^{2}\sqrt{ab}·(-\frac{3}{2}a\sqrt{ab})÷(3×\frac{\sqrt{ab}}{a})$
$=2b\sqrt{ab}·(-\frac{3}{2}a\sqrt{ab})×\frac{a}{3\sqrt{ab}}$
$=2b×(-\frac{3}{2}a)×\frac{a}{3}×\sqrt{ab}×\sqrt{ab}÷\sqrt{ab}$
$=-a^{2}b×\sqrt{ab}$
$=-a^{2}b\sqrt{ab}$
