Question: The difference of the two perfect cubes is 387. If the cube root of the greater of two numbers is 8, find the cube root of the smaller number.
Answer:
Given:
The difference of the two perfect cubes is 387.
The cube root of the greater of two numbers is 8.
To find:
We have to find the cube root of the smaller number.
Assumption:
Let the cube root of the smaller number be x.
So, we need to find the value of x.
Solution:
The difference of the two perfect cubes is 387.
The cube root of the greater of two numbers is 8.
This implies, The greater of the two numbers = Cube of 8 = (8)3= 8 x 8 x 8 = 512.
Let the smaller number be x3.
Therefore,
512 - x3 = 387
or - x3 = 387 - 512
or - x3 = - 125
or x3 = 125
or x3 = 53
or x = 5
Hence, This implies, The cube root of the smaller number is 5.
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