Question

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

Answer 1

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.

Answer 2

Hey, mate here is your AnsweR.

To find :-

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

Solution :-

First we find the factors of 5400 by division method.

See the attachment.

➯ 5400 =2×2×2×5×5×3×3×3

➠ 5400 = 2³ × 3³ × 5²

Here, 5 occurs only two times

When 5 is multiplied to 5400, it will become a perfect cube.

➠ 27000=2³ × 3³ × 5³

Now, the factorization of 27000 contains product of cubes of all its factors.

∴The required smallest number is 5.

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