| Difference of two perfect cubes is 189. If the cube root of the smaller of the two numbers is 3, find the cube root of the larger number. |
A) 4
B) 6
C) 8
D) 10
Correct Answer: B
Solution :
Let the larger perfect cube be \[{{x}^{3}}\] and smaller perfect cube be \[{{y}^{3}}\] According to question, \[{{x}^{3}}-{{y}^{3}}=189~~~~~~~~...(i)\] Also, \[\sqrt[3]{{{y}^{3}}}=3\Rightarrow {{y}^{3}}={{3}^{3}}=27\] \[{{x}^{3}}-27=189\] \[[from\,\,(i)]\] \[\Rightarrow {{x}^{3}}=189+27=216\] \[\Rightarrow x=\sqrt[3]{216}\] \[216=\underline{2\times 2\times 2}\times \underline{3\times 3\times 3}={{(2\times 3)}^{3}}\] \[\Rightarrow \sqrt[3]{216}=2\times 3=6\] \[\therefore x=\sqrt[3]{216}=6\] \[\because \] Larger Perfect cube is \[{{x}^{3}}\]. \[\therefore \] Its cube root is \[\sqrt[3]{{{x}^{3}}}=x=6\] \[\therefore \] Its cube root is \[\sqrt[3]{{{x}^{3}}}=x=6\]
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