Question

11．計(jì)算：2$\sqrt{3}$×$\root{3}{1.5}$×$\root{6}{12}$．

Answer 1

分析 利用根式的性質(zhì)結(jié)合積的乘方運(yùn)算法則化簡(jiǎn)各式求出即可．

解答 解：原式=$\sqrt{12}$×（$\frac{9}{4}$）${\;}^{\frac{1}{6}}$×12${\;}^{\frac{1}{6}}$
=（12³）${\;}^{\frac{1}{6}}$×（$\frac{9}{4}$）${\;}^{\frac{1}{6}}$×12${\;}^{\frac{1}{6}}$
=（12³×$\frac{9}{4}$×12）${\;}^{\frac{1}{6}}$
=（12³×3³）${\;}^{\frac{1}{6}}$
=（3³×4³×3³）${\;}^{\frac{1}{6}}$
=（6⁶）${\;}^{\frac{1}{6}}$
=6．

點(diǎn)評(píng) 此題主要考查了實(shí)數(shù)運(yùn)算，正確利用根式的性質(zhì)化簡(jiǎn)各式是解題關(guān)鍵．