. Find the smallest number by which the following must be divided to make it a perfect cube. And
estimate the cube root of the perfect cube so obtained.
(a) 725
(b) 550
(c) 1375
(d) 1824
Answers
ANSWER ⤵️
a) 725
Prime factors of 725 :-
→ 725 = 5 * 5 * 29
now, as we can see both 5 and 29 prime factors are 2 times and 1 time only .
in order to be a perfect cube a number must have pair of 3.
Therefore, we can conclude that, we have to remove all 5 and 29 .
Hence,
→ smallest Number by which divide to make a perfect cube is = 5 * 5 * 29 = 725 .
and, than ,
→ Result will be a perfect cube of = (725/725) = 1 .
b) 550
Prime factors of 550 :-
→ 550 = 2 * 5 * 5 * 11
now, as we can see again none of the prime factors is in the pair of 3.
in order to be a perfect cube a number must have pair of 3.
Therefore, we can conclude that, we have to remove prime factors .
Hence,
→ smallest Number by which divide to make a perfect cube is = 550 .
and, than ,
→ Result will be a perfect cube of = (550/550) = 1 .
c) 1375
Prime factors of 1375 :-
→ 1375 = 5 * 5 * 5 * 11
now, as we can see here 5 is in the pair of three. none of the prime factors is in the pair of 3.
Therefore, we can conclude that, we have to remove only 11 to make a perfect cube .
Hence,
→ smallest Number by which divide to make a perfect cube is = 11 .
and, than ,
→ Result will be a perfect cube of = (1375/11) = 125 = 5³ => 5 .
D) 1824
Prime factors of 1824 :-
→ 1824 = (2 * 2 * 2) * 2 * 2 * 3 * 19
as we can see here only 2 have one pair of 3.
Therefore, we need to remove rest prime factors to make a perfect cube .
Hence,
→ smallest Number by which divide to make a perfect cube is = 2 * 2 * 3 * 19 = 228 .
and, than ,