Question

12．$（\frac{π-3}{4}{）^0}+\sqrt{2}•（0.25{）^{0.25}}+lg5•lg20+{（lg2）^2}$=3．

Answer 1

分析 化0指數(shù)冪為1，化小數(shù)為分?jǐn)?shù)，然后利用有理指數(shù)冪的運(yùn)算性質(zhì)和對(duì)數(shù)的運(yùn)算性質(zhì)化簡求值．

解答 解：$（\frac{π-3}{4}{）^0}+\sqrt{2}•（0.25{）^{0.25}}+lg5•lg20+{（lg2）^2}$
=1+${2}^{\frac{1}{2}}•$$（\frac{1}{4}）^{\frac{1}{4}}$+lg5（2lg2+lg5）+（lg2）²
=1+${2}^{\frac{1}{2}}•$${2}^{-\frac{1}{2}}$+lg5•lg2+lg5+（lg2）²
=2+lg2（lg5+lg2）+lg5
=2+lg2+lg5
=3．
故答案為：3．

點(diǎn)評(píng) 本題考查有理指數(shù)冪的運(yùn)算性質(zhì)，考查了對(duì)數(shù)的運(yùn)算性質(zhì)，是基礎(chǔ)的計(jì)算題．