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A number is a perfect cube only when each factor in the prime factorization of the given number exists in triplets. Using this concept, the smallest number can be identified. (i) 243  243 = 3 × 3 × 3 × 3 × 3 = 33 × 32 Here, one group of 3's is not existing as a triplet. To make it a triplet, we need to multiply by 3. Thus, 243 × 3 = 3 × 3 × 3 × 3 × 3 × 3 = 729 is a perfect cube Hence, the smallest natural number by which 243 should be multiplied to make a perfect cube is 3. (ii) 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 23 × 23 × 2 × 2 Here, one of the groups of 2’s is not a triplet. To make it a triplet, we need to multiply by 2. Thus, 256 × 2 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 512 is a perfect cube Hence, the smallest natural number by which 256 should be multiplied to make a perfect cube is 2. (iii) 72 72 = 2 × 2 × 2 × 3 × 3 = 23 × 32 Here, the group of 3’s is not a triplet. To make it a triplet, we need to multiply by 3. Thus, 72 × 3 = 2 × 2 × 2 × 3 × 3 × 3 = 216 is a perfect cube Hence, the smallest natural number by which 72 should be multiplied to make a perfect cube is 3. (iv) 675 675 = 5 × 5 × 3 × 3 × 3 = 52 × 33 Here, the group of 5’s is not a triplet. To make it a triplet, we need to multiply by 5. Thus, 675 × 5 = 5 × 5 × 5 × 3 × 3 × 3 = 3375 is a perfect cube Hence, the smallest natural number by which 675 should be multiplied to make a perfect cube is 5. (v) 100 100 = 2 × 2 × 5 × 5 = 22 × 52 Here both the prime factors are not triplets. To make them triplets, we need to multiply by one 2 and one 5. Thus, 100 × 2 × 5 = 2 × 2 × 2 × 5 × 5 × 5 = 1000 is a perfect cube Hence, the smallest natural number by which 100 should be multiplied to make a perfect cube is 2 × 5 =10 ☛ Check: NCERT Solutions for Class 8 Maths Chapter 7 Video Solution: Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube. (i) 243 (ii) 256 (iii) 72 (iv) 675 (v) 100NCERT Solutions for Class 8 Maths Chapter 7 Exercise 7.1 Question 2 Summary: The smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.(i) 243 (ii) 256 (iii) 72 (iv) 675 (v) 100 are (i) 3, (ii) 2, (iii) 3, (iv) 5, and (v) 10 ☛ Related Questions:
Which least number must be multiplied to 243 to make it a perfect cube?Therefore, 243 must be multiplied by 3 to make it a perfect cube. Here one factor 2 is required to make a 3's group. Therefore, 256 must be multiplied by 2 to make it a perfect cube.
What is the smallest number by which 243 should be multiplied to make the product a perfect cube also find the cube root of the product?If another 3 is multiplied to the number 243, then the resulting number would become a perfect cube. So in order to make the number 243 a perfect cube, it has to be multiplied with the number 3. Hence the smallest number to be multiplied to the number 243 is 3, in order to make the number 243 a perfect cube.
IS 243 a perfect square give reasons?Therefore 243 does not have a number, which when multiplied by itself gives 243. Hence 243 is not a perfect square and it does not have a perfect square root.
What number should 3 * be multiplied so that the product is 243?1 Answer. If we multiply 34 by 3 we get 243.
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