Question

The difference of two perfect cones is 189.If the number is 3 find the cube number of the larger number

Answer 1

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Correct question :-

The difference of two perfect cubes is 189.If the cube root of smaller number is 3 find the cube root of the larger number

Given :-

• The difference of two perfect cubes is 189.
• The cube root of smaller number is 3

To find :-

• The cube root of the larger number.

Solution :-

Let the cube root of the larger number be x.

Let the cube root of the smaller number be y.

As per first condition :-

• The difference of two perfect cubes is 189

Representing it mathematically.

x³ - y³ = 189 ----> 1

As per the second condition :-

• the cube root of the smaller number is 3

y = 3

Let's calculate the cube of 3

Cube of 3 i.e y³ = 3³ = 3 × 3 × 3 = 27

•°• y³ = 27

Substitute y = 27 in equation 1,

x³ - 27 = 189

x³ = 189 + 27

x³ = 216

x = ³√216

x = 6

•°• Cube root of the larger number, x = 6

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Cube of 3 = 27 = x

Cube of 6 = 216 = y

Difference = 189

y - x = 189

216 - 27 = 189

189 = 189

LHS = RHS.

Hence verified.