What is the smallest number by which 6912 may be divided so that the product is a perfect cube?
|
Solution: Show
Nội dung chính
A number is a perfect cube only when each factor in the prime factorization is grouped in triples. Using this concept, the smallest number can be identified. (i) 81  81 = 3 × 3 × 3 × 3 = 33 × 3 Here, the prime factor 3 is not grouped as a triplet. Hence, we divide 81 by 3, so that the obtained number becomes a perfect cube. Thus, 81 ÷ 3 = 27 = 33 is a perfect cube. Hence the smallest number by which 81 should be divided to make a perfect cube is 3. (ii) 128 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 23 × 23 × 2 Here, the prime factor 2 is not grouped as a triplet. Hence, we divide 128 by 2, so that the obtained number becomes a perfect cube. Thus, 128 ÷ 2 = 64 = 43 is a perfect cube. Hence the smallest number by which 128 should be divided to make a perfect cube is 2. (iii) 135 135 = 3 × 3 × 3 × 5 = 33 × 5 Here, the prime factor 5 is not a triplet. Hence, we divide 135 by 5, so that the obtained number becomes a perfect cube. 135 ÷ 5 = 27 = 33 is a perfect cube. Hence the smallest number by which 135 should be divided to make a perfect cube is 5. (iv) 192 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3 = 23 × 23 × 3 Here, the prime factor 3 is not grouped as a triplet. Hence, we divide 192 by 3, so that the obtained number becomes a perfect cube. 192 ÷ 3 = 64 = 43 is a perfect cube Hence the smallest number by which 192 should be divided to make a perfect cube is 3. (v) 704 704 = 2 × 2 × 2 × 2 × 2 × 2 × 11 = 23 × 23 × 11 Here, the prime factor 11 is not grouped as a triplet. Hence, we divide 704 by 11, so that the obtained number becomes a perfect cube. Thus, 704 ÷ 11 = 64 = 43 is a perfect cube Hence the smallest number by which 704 should be divided to make a perfect cube is 11. ☛ Check: NCERT Solutions for Class 8 Maths Chapter 7 Video Solution: Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube (i) 81 (ii) 128 (iii) 135 (iv) 192 (v) 704NCERT Solutions for Class 8 Maths Chapter 7 Exercise 7.1 Question 3 Summary: The smallest number by which each of the following numbers must be divided to obtain a perfect cube (i) 81 (ii) 128 (iii) 135 (iv) 192 (v) 704 are (i) 3, (ii) 2, (iii) 5, (iv) 3, and (v) 11 ☛ Related Questions:
Course NCERT Class 12Class 11Class 10Class 9Class 8Class 7Class 6 IIT JEE Exam JEE MAINSJEE ADVANCEDX BOARDSXII BOARDS NEET Neet Previous Year (Year Wise)Physics Previous YearChemistry Previous YearBiology Previous YearNeet All Sample PapersSample Papers BiologySample Papers PhysicsSample Papers Chemistry Download PDF's Class 12Class 11Class 10Class 9Class 8Class 7Class 6 Exam CornerOnline ClassQuizAsk Doubt on WhatsappSearch DoubtnutEnglish DictionaryToppers TalkBlogJEE Crash CourseAbout UsCareerDownloadGet AppTechnothlon-2019 Logout Login Register now for special offers +91 Home > English > Class 9 > Maths > Chapter > L.c.m And H.c.f > By which smallest number 6912 ... Text Solution 2346 Answer : C 643177957 0 5.9 K 3:08 6912 को किस छोटी-से-छोटी संख्या से गुणा करें कि गुणनफल पूर्ण घन हो ? 643168017 0 7.6 K 2:28 985527 में किस छोटी - से - छोटी संख्या से भाग दें कि संख्या पूर्ण घन बन जाए ? 643831597 200 7.3 K 2:14 What is a smallest number by which 1600 is to be divided so that the quotient is a perfect cube? 646927611 0 6.8 K 2:00 The smallest number by which 243000 be divided so that the quotient is a perfect cube is 648147463 100 1.3 K क्या 1188 एक पूर्ण घन है ? यदि नहीं तो किस सबसे छोटी प्राकृत संख्या से 1188 को भाग दिया जाये कि भागफल एक पूर्ण घन संख्या प्राप्त हो जाए ? 643789790 0 7.4 K 4:22 Find the smallest number by which `10368` be divided, so that the result is a perfect square. Also, find the square root of the resulting number. Show More Comments Add a public comment... Follow Us: Popular Chapters by Class: Class 6 AlgebraBasic Geometrical IdeasData HandlingDecimalsFractions Class 7 Algebraic ExpressionsComparing QuantitiesCongruence of TrianglesData HandlingExponents and Powers Class 8 Algebraic Expressions and IdentitiesComparing QuantitiesCubes and Cube RootsData HandlingDirect and Inverse Proportions Class 9 Areas of Parallelograms and TrianglesCirclesCoordinate GeometryHerons FormulaIntroduction to Euclids Geometry Class 10 Areas Related to CirclesArithmetic ProgressionsCirclesCoordinate GeometryIntroduction to Trigonometry Class 11 Binomial TheoremComplex Numbers and Quadratic EquationsConic SectionsIntroduction to Three Dimensional GeometryLimits and Derivatives Class 12 Application of DerivativesApplication of IntegralsContinuity and DifferentiabilityDeterminantsDifferential Equations Privacy PolicyTerms And Conditions Disclosure PolicyContact Us What is the perfect cube of 6912?If we look at the number 6912, we know that the cube root is 19.048812623618, and since this is not a whole number, we also know that 6912 is not a perfect cube. What is the smallest number by which 6912 must be multiplied to make it a perfect square?So,the smallest whole number by which 6912 should be multiplied to make it perfect square is 3. What is the least number by which 6750 must be divided so the quotient is perfect cube?Answer: 2 is the smallest number by which 6750 must be divided to get a perfect cube. The perfect cube number is = 3375 and the cube root is 15. What is the smallest number by which the following should be divided to get a perfect cube 56?Hence, the smallest number by which 135 must be divided to obtain a perfect cube is 5. Is 6912 a perfect cube?If we look at the number 6912, we know that the cube root is 19.048812623618, and since this is not a whole number, we also know that 6912 is not a perfect cube.
Which is the smallest number that must be multiplied with 5400 to make it a perfect cube?We should multiply 5400 with 5 to get a perfect cube.
What smallest number by which 7803 be multiplied with so that the product becomes a perfect cube?Hence, the smallest number by which 7803 must be multiplied to obtain a perfect cube is 17.
What is the smallest number by which 6912 must be multiplied so that the 5 The product is a perfect cube?So , 4 is the smallest no. which must be divided 6912 so that the quotient obtained will be a perfect cube.
|
