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प्रश्न
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.
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उत्तर
Given different of two perfect cubes = 189
And cube root of the smaller number = 3
∴ Cube of smaller number = (3)3 = 27
Let cube root of the larger number be x.
Then, cube of larger number = x3
According to the question,
x3 – 27 = 189
⇒ x3 = 189 + 27
⇒ x3 = 216
⇒ x = `root(3)(216) = root(3)(6 xx 6 xx 6)`
∴ x = 6
Hence, the cube root of the larger number is 6.
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