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Question

Difference of 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.


Solution

Given,
The difference in two cubes $$= 387$$
And, the cube root of the greatest number $$= 8$$
So, the greatest number $$= (8)^3 = 8 \times 8 \times 8 = 512$$
Hence, the second number $$= 512 - 387 = 125$$
Thus,
The cube root of $$125$$ is
$$= \sqrt[3]{125} = \sqrt[3]{5 \times 5 \times 5} = 5$$

Mathematics

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