Question

Q.12 What is the smallest number by which 5,400 must be multiplied to make it a
perfect cube?

AND ALSO EXPLAIN THE ANSWER
​

Answer 1

Answer:

it should be multiplied by 5. take a look in the picture.

pls follow kar do : )

Answer 2

To Find: Smallest number to be multiplied to make it a cube. Thus, to make a group of 3 for 5, we need to multiply 5400 by 5. Answer: The smallest number which is to be multiplied is 5.

Prime factorising 5400, we get,

5400=3×3×3×5×5×2×2×2

= 3³ × 2³ × 5²

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.

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