知识点挑题 - 初中数学 - 优优班--学霸训练营

1．
计算：\((-\sqrt{2})\times \sqrt{6}+|\sqrt{3}-2|-{{(\dfrac{1}{2})}^{-1}}\)．

难度：较易

解析收藏试题篮
2．计算：
\((1){{\left( -{{x}^{4}} \right)}^{3}}\div {{\left( -{{x}^{3}} \right)}^{2}}\cdot \left[ {{\left( -x \right)}^{3}}\div {{\left( -x \right)}^{2}} \right]\)

\((2)\)\((7+4\sqrt{3}){{(2-\sqrt{3})}^{2}}+(2+\sqrt{3})(2-\sqrt{3});\)

难度：较易

解析收藏试题篮
3．
计算： \((1)\)\( \sqrt {(-2)^{2}}\) \(+\)\( \sqrt[3]{-8}\)
\((2) \dfrac { \sqrt {27}- \sqrt {12}}{ \sqrt {3}}\)
\((3)\)\( \sqrt {48}\) \(÷\)\( \sqrt {3}\) \(-\)\( \sqrt { \dfrac {1}{2}}\) \(×\)\( \sqrt {12}\) \(+\)\( \sqrt {24}\)
\((4) \sqrt {5}-( \sqrt {3}+ \sqrt {15})÷ \sqrt {6}× \sqrt {2}\)
\((5)( \sqrt {48}-4 \sqrt { \dfrac {1}{8}})-(3 \sqrt { \dfrac {1}{3}}-2 \sqrt {0.5})\)
\((6)(3+ \sqrt {5})(3- \sqrt {5})-( \sqrt {3}-1)^{2}\)

难度：较易

解析收藏试题篮
4．
计算下列各小题：

\((1)(\sqrt{48}-\dfrac{3}{2}\sqrt{3})\div \sqrt[3]{\dfrac{1}{8}}\)；

\((2)(2\sqrt{3}+\sqrt{6})(2\sqrt{3}-\sqrt{6})-{{(\sqrt{2}-1)}^{2}}\)．

难度：较难

解析收藏试题篮
5．计算：
\((1)(-6{)}^{2}- \sqrt{25}+ \sqrt{(-3{)}^{2}} \)；
\((2)( \sqrt{18}- \sqrt{24})÷ \sqrt{6}+(1- \sqrt{3}{)}^{2} \)．

难度：中等

解析收藏试题篮
6． \((\)本题\(8\)分\()(1)\)解方程： \((2)\)

难度：中等

解析收藏试题篮
7．
阅读理解材料：把分母中的根号去掉叫做分母有理化，例如：

\(①\dfrac{2}{\sqrt{5}}=\dfrac{2\sqrt{5}}{\sqrt{5}\cdot \sqrt{5}}=\dfrac{2\sqrt{5}}{5}\)； \(② \dfrac{1}{ \sqrt{2}-1}= \dfrac{1×\left( \sqrt{2}+1\right)}{\left( \sqrt{2}-1\right)\left( \sqrt{2}+1\right)}= \dfrac{ \sqrt{2}+1}{{\left( \sqrt{2}\right)}^{2}-{1}^{2}}= \sqrt{2}+1 \)等运算都是分母有理化。根据上述材料，

\((1)\)化简\((\)分母有理化\()\)：\(\dfrac{1}{\sqrt{3}-\sqrt{2}}\)

\((2)\)化简\((\)分母有理化\()\)：\(\dfrac{1}{\sqrt{n}+\sqrt{n+1}}\)

\((3)\)计算：\(\dfrac{1}{1+\sqrt{3}}+\dfrac{1}{\sqrt{3}+\sqrt{5}}+\dfrac{1}{\sqrt{5}+\sqrt{7}}+\cdots +\dfrac{1}{\sqrt{2017}+\sqrt{2019}}\)

难度：难

解析收藏试题篮
8．
计算：\(3 \sqrt { \dfrac {1}{3}}×(- \dfrac {1}{2} \sqrt {48})-(- \dfrac {1}{ \sqrt {2}})^{-2}+[(-1)^{2014}+( \sqrt {3}-2)^{0}-| \sqrt {3}-2|]÷ \sqrt {12}\)．

难度：易

解析收藏试题篮
9．

计算：

\((1)( \sqrt{24}- \sqrt{2})-( \sqrt{8}+ \sqrt{6}) \)；          \((2) \sqrt{6}× \sqrt{15}× \sqrt{10} \)

\((3)\) \( \sqrt{(2+ \sqrt{3}{)}^{2005}}× \sqrt{(2- \sqrt{3}{)}^{2005}} \)       \((4) \sqrt{1 \dfrac{2}{3}}÷( \sqrt{2 \dfrac{1}{3}}÷ \sqrt{1 \dfrac{2}{5}}) \)

\(⑸ \sqrt{12}÷( \dfrac{1}{ \sqrt{3}}- \dfrac{1}{ \sqrt{12}}) \)            \(⑹ \dfrac{1}{1+ \sqrt{2}}+ \dfrac{1}{ \sqrt{2}+ \sqrt{3}}+ \dfrac{1}{ \sqrt{3}+ \sqrt{4}}+…+ \dfrac{1}{ \sqrt{99}+ \sqrt{100}} \)

难度：较易

解析收藏试题篮
10． \((1)\)计算：\(2\sin 60^{\circ}-|3\tan 30^{\circ}-2|+( \sqrt {3}-1)^{2}\)
\((2)\)解方程：\((x+1)(x+2)=2x+4\)．

难度：较易

解析收藏试题篮

0/40

进入组卷