What is the smallest number by which 675 must be multiplied so that the products are perfect cubes?
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Text Solution Answer : 5 Related Videos647110493 0 6.3 K 2:07 Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube : 675 642717330 0 4.8 K 1:18 Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube: 675 642956454 0 2.5 K 2:40 Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube. 643099327 0 7.5 K 2:07 Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube : 675 643831607 0 2.0 K 2:11 Find the smallest number by which 8788 must be multiplied to obtain a perfect cube? 643830611 0 5.0 K 7:28 Find the smallest number by which 2116 must be multiplied to obtain a perfect cube ? Show More Comments Add a public comment... 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Find the smallest number by which the following number must be multiplied to obtain a perfect cube: 675 - Get the answer to this question and access a vast question bank that is tailored for students. Academic QuestionsMaths QuestionsFind The Smallest Number By Which The Following Number Must Be Multiplied To Obtain A Perfect Cube 675 Find the smallest number by which the following number must be multiplied to obtain a perfect cube: 675We have to find the smallest number by which 675 must be multiplied to obtain a perfect cube Solution 675 On prime factorisation of 675 we get, 675 = 3×3×3×5×5 By assorting the factors in triplets of equal factors, 675 = (3×3×3) x 5×5 Here, 5 cannot be arranged into triplets of equal factors. ∴ We will multiply 675 by 5 to get perfect cube. Answer The smallest number by which 675 must be multiplied to obtain a perfect cube is 5. Was this answer helpful? 4 (23) Related Questions & Answers Which State Of India Is The Leading Producer Of Linseed What Is Lateral Displacement What Is The Efficiency Of Fuel Cell The Scientific Notation For 000016 Is What Is The Modern Periodic Table Name The Contents That Are Present In The Bile Pigment The Physical Properties Of Isotopes Differ Due To How Does The Light Coming From An Object Enter The Eye What Are The Different Types Of Insulators What Are The Demerits Of Chemical Equation स्रोत : byjus.com What is the smallest number by which 675 must be multiplied so that the product is a perfect cube?Click here👆to get an answer to your question ✍️ What is the smallest number by which 675 must be multiplied so that the product is a perfect cube? Question What is the smallest number by which 675 must be multiplied so that the product is a perfect cube?Medium Open in App Updated on : 2022-09-05 Solution Verified by Toppr Correct option is A) Prime factorising 675, we get, 675=5×5×3×3×3 =3 3 ×5 2 . We know, a perfect cube has multiples of 3 as powers of prime factors. Here, number of 3's is 3 and number of 5's is 2. So we need to multiply another 5 in the factorization to make 675 a perfect cube. Hence, the smallest number by which 675 must be multiplied to obtain a perfect cube is 5. Was this answer helpful? 1144 15 स्रोत : www.toppr.com 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) 100Find 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. The smallest numbers required." 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) 100 Solution: 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 7Video 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) 100 NCERT 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: 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) 704. Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube? Find the cube root of each of the following numbers by prime factorization method. (i) 64 (ii) 512 (iii) 10648 (iv) 27000 (v) 15625 (vi) 13824 (vii) 110592 (viii) 46656 (ix) 175616 (x) 91125 State true or false. (i) Cube of any odd number is even. (ii) A perfect cube does not end with two zeros. (iii) If square of a number ends with 5, then its cube ends with 25. (iv) There is no perfect cube which ends with 8. (v) The cube of a two digit number may be a three digit number. (vi) The cube of a two digit number may have seven or more digits. (vii) The cube of a single digit number may be a single digit number. स्रोत : www.cuemath.com What should be multiplied by 675 to make it a perfect square?This is Expert Verified Answer
Now, pair the prime factors of the number obtained. Since, '3' doesn't have a pair, 675 is not a perfect square. ∴ We need to multiply '3' to 675 to obtain a perfect square.
IS 675 a perfect cube number?∴ The smallest number required to multiply 72 to make it a perfect cube is 3. Grouping the prime factors of 675 to triples, we are left over with 5 × 5. ∴ 675 is not a perfect cube.
What is the cube of 675?The prime factorization of 675 is 3 × 3 × 3 × 5 × 5, hence, the cube root of 675 in its lowest radical form is expressed as 3 ∛25.
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Cube Root of 675.. What is the smallest number 675?so the smallest number by which 675 should be multiplied is 5.
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