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Difference of two perfect cube is $189$. If the cube root of the smaller of the two numbers is $3$, then find the cube root of the larger number.
Given: Difference of two perfect cube is $189$. If the cube root of the smaller of the two numbers is $3$.
To do: To find the cube root of the larger number.
Solution:
Let $x$ and $y$ be the cube roots of the larger and smaller number respectively.
As given difference of two numbers which are perfect cubes is $189$.
$\Rightarrow x^3-y^3=189$
If $y$ is the cube root of the smaller number.
$\Rightarrow y=3$
$\Rightarrow y^3=27$
$\Rightarrow x^3-y^3=189$
$\Rightarrow x^3 -27=189$ [On putting the value of $y^3=27$]
$\Rightarrow x^3=189+27$
$\Rightarrow x^3=216$
$\Rightarrow x=\sqrt[3]{216}$
$\Rightarrow x=\sqrt[3]{6\times6\times6}$
$\Rightarrow x=6$
Therefore, cube root of the larger number is $6$.
Updated on: 10-Oct-2022
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