Difference of two perfect cubes is 189. If the cube root of the smalle

1.	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.
Answer» From the question it is given that, Difference of two perfect cubes = 189 The cube root of the smaller of the two numbers = 3 So, cube of smaller number = 3³ = 3 × 3 × 3 = 27 Let us assume the cube root of larger number be a³ Then, As per the condition given in the question, a³ – 27 = 189 a³ = 189 + 27 a³ =216 By taking cube root on both side, a = ³√216 a = ³√(6 × 6 × 6) a = ³√(6³) a = 6 ∴The cube root of the larger number is 6.

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.

Answer»

From the question it is given that,

Difference of two perfect cubes = 189

The cube root of the smaller of the two numbers = 3

So, cube of smaller number = 3³

= 3 × 3 × 3

= 27

Let us assume the cube root of larger number be a³

Then,

As per the condition given in the question,

a³ – 27 = 189

a³ = 189 + 27

a³ =216

By taking cube root on both side,

a = ³√216

a = ³√(6 × 6 × 6)

a = ³√(6³)

a = 6

∴The cube root of the larger number is 6.