A) \[2-{{(0.5)}^{2}},\sqrt{3},\sqrt[3]{0.008},{{(2.89)}^{0.5}}\]
B) \[\sqrt[3]{0.008},{{(2.89)}^{0.5}},\sqrt{3},2-{{(0.5)}^{2}}\]
C) \[\sqrt[3]{0.008},\sqrt{3},{{(2.89)}^{0.5}}2-{{(0.5)}^{2}}\]
D) \[\sqrt{3},\sqrt[3]{0.008},2-{{(0.5)}^{2}},{{(2.89)}^{0.5}}\]
Correct Answer: B
Solution :
\[~{{\left( 2.89 \right)}^{0.5}}= {{\left( 2.89 \right)}^{1/2}}= 1.7\] \[2 - {{\left( 0.5 \right)}^{2}}= 2 - 0.25 = 1.75\] \[\therefore \]\[\sqrt{3}\] =1.732 (approx.) \[\sqrt[3]{0.008}\] = 0.2 \[\therefore \] 0.2 < 1.7 < 1.732 < 1.75 \[\sqrt[\mathbf{3}]{\mathbf{0}.\mathbf{008}}\text{ }<\text{ }{{\left( \mathbf{2}.\mathbf{89} \right)}^{\mathbf{0}.\mathbf{5}}}<\text{ }\sqrt{\mathbf{3}\text{ }}<\text{ }\mathbf{2}-\text{ }{{\left( \mathbf{0}.\mathbf{5} \right)}^{\mathbf{2}}}\]
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