Question

Question 122

Solve the following question:

Difference of two perfect cubes is 189. If the cube root of the smaller of the two numbers is 3, then find the cube root of the larger number.

Answer 1

Given difference of two perfect cubes = 189
and cube root of the smaller number = 3
$\therefore$ Cube of smaller number $=(3{)}^3=27$
Let cube root of the larger number be $x$
Then, cube of larger number $=x^3$
According to the question,
$x^3-27=189\Rightarrow x^3=189+27\Rightarrow x^3=216\Rightarrow x=\sqrt[3]{3216}=\sqrt[3]{36\times 6\times 6}\therefore x=6$
Hence, the cube root of the larger number is 6.