Question

find the smallest number by which 1600 divided so that the quotient is a perfect cube , further find its cube root​

Answer 1

Answer:

Smallest : 25

Cube root : 4

Step-by-step explanation:

1600÷2=800

800÷2=400

400÷2=200

200÷2=100

100÷2=50

50÷2=25

Hence, (2×2×2) × (2×2×2) = 64

So, 1600 should be divided by 25 to become perfect cube of 4.

Answer 2

Answer:

25 should be divided, 4 will be the cube root

Step-by-step explanation:

1. do prime factorisation of 1600

2. we can see there are 2 triplets formed of 2 and there are only two 5s which doesn't form triplets (factorisation: 2,2,2,2,2,2,5,5)

3. as two 5s are left so 5*5=25

hence 25 should be divided by 1600

the quotient formed is 64 whose cube root is 4