初中数学七年级题库4.20:用九道例题讲全实数的计算类型

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初中数学七年级题库4.20:用九道例题讲全实数的计算类型

1、\(\displaystyle \sqrt{{\frac{9}{4}}}-\sqrt{{49}}\)

原式\(\displaystyle =\frac{3}{2}-7\)

\(\displaystyle =-\frac{{11}}{2}\)

2、\(\displaystyle \sqrt[3]{{-64}}+\sqrt[3]{{27}}-2\sqrt[3]{{-\frac{1}{8}}}\)

原式\(\displaystyle =-4+3-2\times \left( {-\frac{1}{2}} \right)\)

\(\displaystyle =-4+3+1\)

\(\displaystyle =0\)

3、\(\displaystyle -\sqrt{{{{{\left( {-2} \right)}}^{2}}}}-\sqrt{{1\frac{{11}}{{25}}}}+\frac{2}{5}\sqrt[3]{{-125}}\)

原式\(\displaystyle =-\sqrt{4}-\sqrt{{\frac{{36}}{{25}}}}+\frac{2}{5}\times \left( {-5} \right)\)

\(\displaystyle =-2-\frac{6}{5}-2\)

\(\displaystyle =-4-\frac{6}{5}\)

\(\displaystyle =-\frac{{26}}{5}\)

4、\(\displaystyle \sqrt{{{{{\left( {\frac{1}{3}} \right)}}^{2}}}}+\sqrt[3]{{\left( {1-\frac{5}{9}} \right)\left( {\frac{1}{3}-1} \right)}}\)

原式\(\displaystyle =\frac{1}{3}+\sqrt[3]{{\frac{4}{9}\times \left( {-\frac{2}{3}} \right)}}\)

\(\displaystyle =\frac{1}{3}+\sqrt[3]{{-\frac{8}{{27}}}}\)

\(\displaystyle =\frac{1}{3}-\frac{2}{3}\)

\(\displaystyle =-\frac{1}{3}\)

5、\(\displaystyle \sqrt[3]{{{{{\left( {\frac{7}{8}-1} \right)}}^{2}}}}-\sqrt{{{{{\left( {1-\frac{5}{4}} \right)}}^{2}}}}+{{\left| {\pi -3} \right|}^{0}}\)

原式\(\displaystyle =\sqrt[3]{{{{{\left( {-\frac{1}{8}} \right)}}^{2}}}}-\sqrt{{{{{\left( {-\frac{1}{4}} \right)}}^{2}}}}+1\)

\(\displaystyle =\sqrt[3]{{\frac{1}{{64}}}}-\sqrt{{\frac{1}{{16}}}}+1\)

\(\displaystyle =\frac{1}{4}-\frac{1}{4}+1\)

\(\displaystyle =1\)

6、\(\displaystyle 3\sqrt{5}+2\sqrt{5}-\sqrt{5}\)

原式\(\displaystyle =4\sqrt{5}\)

7、\(\displaystyle \sqrt{3}\left( {\sqrt{3}+\frac{1}{{\sqrt{3}}}+2} \right)\)

原式\(\displaystyle =\sqrt{3}\times \sqrt{3}+\sqrt{3}\times \frac{1}{{\sqrt{3}}}+\sqrt{3}\times 2\)

\(\displaystyle =3+1+2\sqrt{3}\)

\(\displaystyle =4+2\sqrt{3}\)

8、\(\displaystyle \sqrt{2}\left( {\sqrt{2}+2} \right)-\left( {3\sqrt{2}-1} \right)\)

原式\(\displaystyle =\sqrt{2}\times \sqrt{2}+2\times \sqrt{2}-3\sqrt{2}+1\)

\(\displaystyle =2+2\sqrt{2}-3\sqrt{2}+1\)

\(\displaystyle =3-\sqrt{2}\)

9、\(\displaystyle \left( {\sqrt{6}-3\sqrt{6}} \right)-\sqrt{6}\left( {\sqrt{6}-\frac{2}{{\sqrt{6}}}-1} \right)\)

原式\(\displaystyle =\sqrt{6}-3\sqrt{6}-6+2+\sqrt{6}\)

\(\displaystyle =-4-\sqrt{6}\)

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