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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.

Solution:

Given, difference of two perfect cubes is 189.

We have to find the cube root of the larger number.

Given, cube root of smaller number = 3

On cubing both sides,

Cube of smaller number = (3)³ = 27

Let the cube root of the larger number be y.

According to the question,

Cube of larger number - cube of smaller number = 189

y³ - 27 = 189

y³ = 189 + 27

y³ = 216

Taking cube root,

y = ∛216

y = ∛(6)³

y = 6

Therefore, the cube root of the larger number is 6.

✦ Try This: Difference of two perfect cubes is 169. If the cube root of the smaller of the two numbers is 4, find the cube root of the larger number.

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 3 Problem 122

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

Summary:

Difference of two perfect cubes is 189. If the cube root of the smaller of the two numbers is 3, the cube root of the larger number is 6.

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