Question

Find the smallest number by which 5400 must be multiplied so that the product is a perfect cube.Also find the cube root of the number obtained.

Answer 1

Step-by-step explanation:

$5400 = 9 \times 600 \\ = 9 \times 60 \times 10 \\ = 9 \times 8 \times 15 \times 5 \\ = 27 \times 8 \times 25$

27 and 8 are perfect cubes

so if we multiply it with 5 , 5400 will become a perfect cube

cuberoot is

$3 \times 2 \times 5 = 30$

Answer 2

Step-by-step explanation:

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. by

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.