Question

find the least no to be multiplied to get a perfect cube . a) 1323 b) 5400 c) 14400 c) 2560​

Answer 1

Answer:

a) 7

b) 30

c) 60

d) 25

Step-by-step explanation:

a) 1323=3×3×3×7×7 = 3³ x 7².

b) by factorising 5400, we get

2×2×2×3×3×3×5×5

logic is, to become a cube, all number should be in pair in three”s

here 2 is in pair, 3 is in pair, 5 can be in pair if multiplied by one more 5

after multiplying 5, it becomes,

2×2×2×3×3×3×5×5×5

hence it is the cube of 2×3×5= 30

c) Prime factors of 14400 are 2,2,2,2,2,2,3,3,5,5. By grouping 3 same numbers we find that group of 3 and 5 are incomplete. So 14400 must be multiplied by 3*5=15. It will be 216000, a cube of 2*2*3*5=60

d) we need to multiply the same number twice to get the perfect cube. Which is 5×52 will make the perfect cube. Hence the smallest number by 2560 number must be multiplied so that the product is a perfect cube is 25.