| The ascending order of \[{{(2.89)}^{0.5}},\]\[2-{{(0.5)}^{2}},\]\[\sqrt{3}\]and\[3\sqrt{0.008}\] is |
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 :
| \[{{(2,89)}^{0.5}}={{(2.89)}^{1/2}}={{[{{(1.7)}^{2}}]}^{1/2}}=1.7\] |
| \[2-{{(0.5)}^{2}}=2-0.25=1.75\] |
| \[\sqrt{3}=1.732\] |
| \[\sqrt[3]{0.008}=0.2\] |
| \[\therefore \]Ascending order is |
| \[\sqrt[3]{0.008}<{{(2.89)}^{0.5}}<\sqrt{3}<2-{{(0.5)}^{2}}\] |
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