Question

answer in deep
what is the smallest number that must be multiplied by 5400 to make it a perfect cube

Answer 1

Answer:

Step-by-step explanation:

by factorizing 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

hope u understand

Answer 2

$5400 = (5 \times 5) \times (2 \times 2 \times 2) \times (3 \times 3 \times 3) \\ 5400 = {5}^{2} \times {2}^{3} \times {3}^{3} \\ \\ \\ all\:numbers\:must\:be\:in\:pair\:of \:three's\\ 5 \: must \: be \: multiplied \: by \: 5400 \: to \\ \: make \: a \: perfect \: cube \\ \\ 5400 \times 5 = 27000 \\ \\ \sqrt[3]{27000} = 30$