Question

7．化簡（$\frac{1}{\sqrt{2}-\sqrt{3}}$）²⁰¹³•（$\frac{1}{\sqrt{2}+\sqrt{3}}$）²⁰¹⁴的結(jié)果是（　�。�

• A． $\sqrt{2}$-$\sqrt{3}$
• B． $\sqrt{2}$+$\sqrt{3}$
• C． -$\sqrt{2}$-$\sqrt{3}$
• D． -$\sqrt{2}$+$\sqrt{3}$

Answer 1

分析 根據(jù)冪的運(yùn)算將原式變形為（$\frac{1}{\sqrt{2}-\sqrt{3}}$）²⁰¹³•（$\frac{1}{\sqrt{2}+\sqrt{3}}$）²⁰¹³•$\frac{1}{\sqrt{2}+\sqrt{3}}$，繼而根據(jù)積的乘方和分母有理化可得答案．

解答 解：原式=（$\frac{1}{\sqrt{2}-\sqrt{3}}$）²⁰¹³•（$\frac{1}{\sqrt{2}+\sqrt{3}}$）²⁰¹³•$\frac{1}{\sqrt{2}+\sqrt{3}}$
=（$\frac{1}{\sqrt{2}+\sqrt{3}}$×$\frac{1}{\sqrt{2}-\sqrt{3}}$）²⁰¹³•$\frac{1}{\sqrt{2}+\sqrt{3}}$
=（-1）²⁰¹³×$\frac{\sqrt{2}-\sqrt{3}}{（\sqrt{2}+\sqrt{3}）（\sqrt{2}-\sqrt{3}）}$
=-1×$\frac{\sqrt{2}-\sqrt{3}}{-1}$
=$\sqrt{2}-\sqrt{3}$，
故選：A．

點(diǎn)評 本題主要考查二次根式的混合運(yùn)算，熟練掌握冪的運(yùn)算法則和分母有理化是解題的關(guān)鍵．