What is the smallest number by which 1296 must be divided so that the quotient is a perfect cube?
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Open in App Solution 2×2×11×11×11=5324 so the smallest natural number should 5324 be divided so that the quotient is a perfect cube is 2×2=4 Ans: 4Similar questions Q. Find the least number by which 5324 should be divided to obtain a perfect square. Also, find the square root of the number so obtained. Q. By what least number by which 3600 be divided to make it a perfect cube Q. By what least number should
1536 be divided to get a perfect cube? Q. Is 9720 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube. Q. The smallest natural number by which 1296 be divided to get a perfect cube is ______. View More (i) We have, 1536 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 After grouping the prime factors in triplets, it’s seen that one factor 3 is left without grouping. 1536 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × 3 So, in order to make it a perfect cube, it must be divided by 3. Thus, the smallest number by which 1536 must be divided to obtain a perfect cube is 3. (ii) We have, 10985 = 5 × 13 × 13 × 13 After grouping the prime factors in triplet, it’s seen that one factor 5 is left without grouping. 10985 = 5 × (13 × 13 × 13) So, it must be divided by 5 in order to get a perfect cube. Thus, the required smallest number is 5. (iii) We have, 28672 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 7 After grouping the prime factors in triplets, it’s seen that one factor 7 is left without grouping. 28672 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × 7 So, it must be divided by 7 in order to get a perfect cube. Thus, the required smallest number is 7. (iv) 13718 = 2 × 19 × 19 × 19  After grouping the prime factors in triplets, it’s seen that one factor 2 is left without grouping. 13718 = 2 × (19 × 19 × 19) So, it must be divided by 2 in order to get a perfect cube. Thus, the required smallest number is 2. Free CT 1: Growth and Development - 1 10 Questions 10 Marks 10 Mins Calculation: 1296 = 6 × 6 × 6 × 6 ⇒ 1296 should be multiplied by 36 to make a perfect cube number. According to the question: ⇒ 36/2 = 18 ∴ The half of the smallest number by which 1296 must be multiplied, So that the product becomes a perfect cube is 18. 1296 × 36 = 46656 46656 is a perfect cube of 36. The correct option is 2 i.e. 18 Last updated on Sep 29, 2022 REET 2022 Written Exam Result Out on 29th September 2022! The final answer key was also out with the result. The exam was conducted on 23rd and 24th July 2022. The candidates must go through the REET Result 2022 to get the direct link and detailed information on how to check the result. The candidates who will be finally selected for 3rd Grade Teachers are expected to receive Rs. 23,700 as salary. Then, the candidates will have to serve the probation period which will last for 2 years. Also, note during probation, the teachers will receive only the basic salary. Is 1296 is a perfect cube?Answer : 1296 is not a perfect cube.
What should be multiplied by 1296 to make perfect cube?⇒ 1296 should be multiplied by 36 to make a perfect cube number. ∴ The half of the smallest number by which 1296 must be multiplied, So that the product becomes a perfect cube is 18. 46656 is a perfect cube of 36. REET 2022 Written Exam Result Out on 29th September 2022!
What is the smallest number by which 12096 should be divided so that the quotient is a perfect cube?Hence, 7 is the smallest number that should be divide 12096 to make it a perfect cube.
What is the smallest number by which 392 should be divided so that the quotient is a perfect cube?Hence, 7 is the smallest number that should be multiplied to 392 to give a perfect cube.
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