Question

20．計(jì)算$\frac{1+\sqrt{2013}（\sqrt{2012}-\sqrt{2011}）}{\sqrt{2011}+\sqrt{2012}+\sqrt{2013}}$+$\sqrt{2011}$=（　�。�

• A． $\sqrt{2010}$
• B． $\sqrt{2011}$
• C． $\sqrt{2012}$
• D． $\sqrt{2013}$

Answer 1

分析 先通分，合并后把分子部分提$\sqrt{2012}$，然后約分即可．

解答 解：原式=$\frac{1+\sqrt{2013}•\sqrt{2012}-\sqrt{2013}•\sqrt{2011}+\sqrt{2011}•\sqrt{2011}+\sqrt{2011}•\sqrt{2012}+\sqrt{2011}•\sqrt{2013}}{\sqrt{2011}+\sqrt{2012}+\sqrt{2013}}$
=$\frac{2012+\sqrt{2012}•\sqrt{2013}+\sqrt{2011}•\sqrt{2012}}{\sqrt{2011}+\sqrt{2012}+\sqrt{2013}}$
=$\frac{\sqrt{2012}（\sqrt{2011}+\sqrt{2012}+\sqrt{2013}）}{\sqrt{2011}+\sqrt{2012}+\sqrt{2013}}$
=$\sqrt{2012}$．
故選C．

點(diǎn)評(píng) 本題考查了二次根式的化簡(jiǎn)求值：二次根式的化簡(jiǎn)求值，一定要先化簡(jiǎn)再代入求值．二次根式運(yùn)算的最后，注意結(jié)果要化到最簡(jiǎn)二次根式，二次根式的乘除運(yùn)算要與加減運(yùn)算區(qū)分，避免互相干擾．