Question

2. Find the smallest number by which each of the following numbers must be multiplied
(i) 72
to obtain a perfect cube.
(ü) 256
(iv) 675
1) 243
100​

Answer 1

Answer:

Question:-

  · Find the smallest number by which each of the following numbers must be multiplied  to obtain a perfect cube.

(i) 72

(ii)256

(iii)675

(iv)243

(v)1000

Solution:-

(i)72

⇒ Prime factor of 72 = 2 × 2 × 2 × 3 × 3

⇒ Prime factor of 72 = $2^{3}$ × 3 × 3

The required smallest number to be multiplied is 3.

(ii)256

⇒ Prime factor of 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

⇒ Prime factor of 256 = $2^{3}$ ×

The required smallest number to be multiplied is 2.

(iii)675

⇒ Prime factor of 675 = 3 × 3 × 3 × 5 × 5

⇒ Prime factor of 675 = $3^{3}$ × 5 × 5

The required smallest number to be multiplied is 5.

(iv) 243

⇒ Prime factor of 243 = 3 × 3 × 3 × 3 × 3

⇒ Prime factor of 243 = $3^{3}$ × 3 × 3

The required smallest number to be multiplied is 3.

(v)100

⇒ Prime factor of 100 = 2 × 2 × 5 × 5

The required smallest number to be multiplied is 2 × 5 = 10.