Question

Find the smallest number by which the following must be divided to make it a perfect cube. And hence estimate the cube root of the perfect cube so obtained. (a) 725 (b) 550 (c) 1375 (d) 1824 please............ solve i. (Answers) (a) 4, 9 (b) 38, 8 (c) 44, 11 (d) 96, 12 ​

Answer 1

Given :- Find the smallest number by which the following must be divided to make it a perfect cube. And hence estimate the cube root of the perfect cube so obtained. (a) 725 (b) 550 (c) 1375 (d) 1824

Solution :-

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 ,

→ Result will be a perfect cube of = (1824/228) = 8 = 2³ => 2 .

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Answer 2

Answer:

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