Question

Find the smallest number by which 17,496
must
divided so that it becomes a
Perfect cube . Also find cube
root
of the number this obtained​

Answer 1

Hey Anjali !

Answer:

Hence the smallest number by which 17496 must be divided so that it becomes a perfect cube is 3.

Cube root of the number obtained is 18.

Step-by-step explanation:

17496

= 2 × 8748

= 2² × 4374

= 2³ × 2187

= 2³ × 3 × 729

= 2³ × 3² ×243

= 2³ × 3³ × 81

= 2³ × 3³ × 3⁴

= 2³ × 3⁷

∴ 17496 = 2³ × 3⁷

If it is divided by 3,

$\frac{17496}{3}$ = 2³ × 3⁶ = (2 × 3²)³

Hence it is a perfect cube.

5832 = (2 × 3²)³

∴ 5832 = (18)³

Hence the smallest number by which 17496 must be divided so that it becomes a perfect cube = 3.

Cube root of the number obtained = 18.

Thanks !