| (i) \[\sqrt[3]{\frac{0.027}{0.008}}\div \sqrt[3]{\frac{0.729}{0.512}}-\frac{1}{3}\] |
| (ii) \[\sqrt[3]{343}+\sqrt[3]{0.064}-\sqrt[3]{0.125}\] |
| (iii) \[\left[ \left( \sqrt[3]{\frac{-216}{42875}}+\sqrt[3]{\frac{64}{125}} \right) \right]\times \sqrt[3]{\frac{343}{1331}}\] |
A)
(i) (ii) (iii) 1 6.9 \[\frac{2}{5}\]
B)
(i) (ii) (iii) 3 7.1 \[\frac{1}{5}\]
C)
(i) (ii) (iii) 4 7.9 \[\frac{2}{5}\]
D)
(i) (ii) (iii) 1 6.5 \[\frac{1}{5}\]
Correct Answer: A
Solution :
We have, (i) \[\sqrt[3]{\frac{0.027}{0.008}}\div \sqrt[3]{\frac{0.729}{0.512}}-\frac{1}{3}\] \[=\sqrt[3]{\frac{0.3\times 0.3\times 0.3}{0.2\times 0.2\times 0.2}}\div \sqrt[3]{\frac{0.9\times 0.9\times 0.9}{0.8\times 0.8\times 0.8}}-\frac{1}{3}\] \[=\left( \frac{0.3}{0.2}\div \frac{0.9}{0.8} \right)-\frac{1}{3}=\left( \frac{0.3}{0.2}\times \frac{0.8}{0.9} \right)-\frac{1}{3}\] \[=\frac{4}{3}-\frac{1}{3}=1\] (ii) We have, \[\sqrt[3]{343}+\sqrt[3]{0.064}-\sqrt[3]{0.125}\] \[-\sqrt[3]{0.5\times 0.5\times 0.5}\] \[=7+0.4-0.5=7-0.1=6.9\] (iii) We have, \[\left[ \left( \sqrt[3]{\frac{-216}{42875}}+\sqrt[3]{\frac{64}{125}} \right) \right]\times \sqrt[3]{\frac{343}{1331}}\] \[=\left[ {{\left( \frac{(-6)\times (-6)\times (-6)}{35\times 35\times 35} \right)}^{\frac{1}{3}}}+{{\left( \frac{4\times 4\times 4}{5\times 5\times 5} \right)}^{\frac{1}{3}}} \right]\] \[\times {{\left( \frac{7\times 7\times 7}{11\times 11\times 11} \right)}^{\frac{1}{3}}}\] \[=\left( \frac{-6}{35}+\frac{4}{5} \right)\times \left( \frac{7}{11} \right)=\left( \frac{-6+28}{35} \right)\times \frac{7}{11}\] \[=\frac{22}{35}\times \frac{7}{11}=\frac{2}{5}\]
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