By which smallest number must 5400 be multiplied to make it a perfect

1.	By which smallest number must 5400 be multiplied to make it a perfect Cube ?
Answer» ong>ANSWER: Step-by-step EXPLANATION: CORRECT option is C 5 Prime factorising 5400, we get, 5400=3×3×3×5×5×2×2×2 =2 3 ×3 3 ×5 2 . We know, a perfect cube has multiples of 3 as powers of prime factors. Here, number of 2's is 3, number of 3's is 3 and number of 5's is 2. So we need to multiply another 5 to the factorization to make 5400 a perfect cube. HENCE, the smallest number by which 5400 must be multiplied to obtain a perfect cube is 5. Therefore, option C is correct.

By which smallest number must 5400 be multiplied to make it a perfect Cube ?

Answer»

Step-by-step EXPLANATION:

CORRECT option is

Prime factorising 5400, we get,

5400=3×3×3×5×5×2×2×2

×3

×5

We know, a perfect cube has multiples of 3 as powers of prime factors.

Here, number of 2's is 3, number of 3's is 3 and number of 5's is 2.

So we need to multiply another 5 to the factorization to make 5400 a perfect cube.

HENCE, the smallest number by which 5400 must be multiplied to obtain a perfect cube is 5.

Therefore, option C is correct.