Question: The difference of the 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.

Answer:

Given:

The difference of two perfect cube is 189.

If the cube root of the smaller of the two numbers is 3.

To Find:

We have 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 the difference of two numbers which are perfect cubes is 189.

=> x^{3} - y^{3} = 189

If y is the cube root of the smaller number.

Then y = 3,

Thus, x3 - 3^{3} = 187 [putting y = 3]

or x^{3} = 187 + 3^{3}

or x^{3} = 187 + (3 x 3 x 3)

or x^{3} = 187 + 27

or x^{3} = 216

or x3 = 6^{3}

or x = 6

Therefore, cube root of the larger number is 6.

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