What is the smallest number by which 3087 may be multiplied so that the product is perfect cube?
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(i) 243 Prime factors of 243 = Here 3 do not appear in 3’s group. Therefore, 243 must be multiplied by 3 to make it a perfect cube.  (ii) 256 Prime factors of 256 = 2\times2\times2\times2\times2\times2\times2\times2 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. (iii) 72 Prime factors of 72 = 2\times2\times2\times3\times3 Here 3 does not appear in 3’s group. Therefore, 72 must be multiplied by 3 to make it a perfect cube. (iv) 675 Prime factors of 675 = 3\times3\times3\times5\times5 Here factor 5 does not appear in 3’s group. Therefore 675 must be multiplied by 3 to make it a perfect cube. (v) 100 Prime factors of 100 = 2\times2\times5\times5 Here factor 2 and 5 both do not appear in 3’s group. Therefore 100 must be multiplied by 2\times5= 10 to make it a perfect cube. Hence, the smallest number by which 3087 must be multiplied to obtain a perfect cube is 3. Is 3087 a perfect cube?Since the prime factor '3' does not form a triplet , hence the given number is not a perfect cube. Which of the following are perfect cube 3087?Since the number 3 has not triplet, Therefore we need to multiply 3087 by 3 to make it a perfect cube. What is the smallest number by which must be multiplied so that the product is a perfect cube?Hence, the smallest number by which 107811 must be multiplied to obtain a perfect cube is 32=9. What is the smallest number by which 2048 may be multiplied so that the product is a perfect cube?Answer. ⇒ √4096=64. Cubes and Cube roots |What is the smallest number by which 3087 can be multiplied...
Is 2048 a perfect square?Hence, 2048 is not a perfect square. What is the smallest number that 484 must be multiplied by to make it a perfect cube?R D Sharma - Mathematics 9 now, in order to be a perfect cube , all prime numbers must have a power of 3 . hence, we have to multiply the given product by 484 to get a perfect cube number. What is the smallest number by which the following number must be multiplied so that the product are perfect cube 35721?Thus, 35721 should be multiplied by 7 to make it a perfect cube. What is the smallest number which when multiplied by 72 the product is a multiple of 112?Answer: Option C - Required number is divisible by 72 as well as by 112, If it is divisible by their L.C.M, which is 1008. Which is the smallest number by which 5324 is multiplied so that the product is a perfect cube also find the cube root of the new number obtained?In the above factorization, 11 occurs thrice and 2 occurs twice. Hence, in order to make the perfect cube we need an extra 2 so that it becomes 2^3. Hence, we have to multiply the given number by 2 to make a perfect cube. What is the smallest number by which 106480 may be multiplied so that the product is a perfect cube?Answer. So the smallest number by which 106480 can be multiplied to become a perfect cube is 100. What is the smallest number by which 392 may be divided so that the quotient is a perfect cube?Hence, the smallest number by which 392 must be multiplied to obtain a perfect cube is 7. What smallest number must be multiplied in the denominator so that the decimal number 14588 625 will be terminated?Multiply (2)3 for making in power of 10 to denominator. denominator is of the form 2m x 5n. So, 14588/625 is the decimal terminating expansion. What is the smallest number by which 35721 must be divided so that quotient is a perfect cube also find the cube root of resulting number?(vii) 35721 Hence, 35721 is not a perfect cube. We divide it by 72 = 49 to make the quotient a perfect cube, which gives 729 as quotient which is a perfect cube. Hence, 49 is the required smallest number. What is the smallest number by which 10976 must be divided to make it a perfect cube?Answer. Answer: the smallest number by which 10976 must be multiplied to obtain a perfect cube is 2. What number must be multiplied to 54 to make it a perfect cube?We need to find factors of 54 first. So,number 2 triplet are not formed. So, to make it a perfect cube we should multiply it by 2*2 = 4. Hope It Helps You! What is the smallest number that 3025 must be multiplied by to make it a perfect cube?So if we multiply 275 by 11, this will give the perfect square 55x55 = 3025. There are no perfect cubes obtained by multiplying 275 by numbers less than 11, so the answer is 11. What smallest number should 7803 be multiplied with 30 that is the product becomes a perfect cube?Hence, 17 is the smallest number which is to be multiplied to the given number for perfect cube. What smallest number should be subtracted from 9805 so that it is divisible by 8?Answer with explanation: On dividing 9805 by 8, the remainder is 5. So, 5 is the smallest number which should be subtracted from 9805 to make it divisible by 8. What is the prime factor of 2048?Factors of 2048 are numbers that, when multiplied in pairs give the product as 2048. There are 12 factors of 2048 of which 2048 itself is the biggest factor and its prime factors are 2 The Prime Factorization of 2048 is 211. What is the smallest number by which you can divide 20328 so that the quotient is a perfect square?Hence, the correct answer is 2. Was this answer helpful? What number should be multiplied to the square root of 64800 to make it a perfect square root?So, √2 should be multiplied to the square root of 64800 to make it a perfect square root. What is the smallest number by which 3087 must be divided so that the quotient is a perfect cube also find the cube root of the quotient so obtained?Answer: 3 is the smallest number by which 3087 must be divided so that the quotient is a perfect cube. What is the least number by which 6750 may be divided so that the quotient is a perfect cube?Answer: 2 is the smallest number by which 6750 must be divided to get a perfect cube. Is 3087 a perfect cube?There are three 7's but only two 3's so 3087 is not a perfect cube. What is the smallest number by which 13122 must be divided to make a perfect cube?Which implies, 18 is the required smallest number by which 13122 should be divided in order to get a perfect cube as the quotient. What is the perfect cube of 3087?Step-by-step explanation:
Since the number 3 has not triplet, Therefore we need to multiply 3087 by 3 to make it a perfect cube.
What is the smallest number by which 3087 must be divided so that the quotient is a perfect cube *?And, it can be removed by dividing it by that number. And, we obtain a perfect cube, as $7 \times 7 \times 7 = 343$ and $\sqrt[3]{{343}} = 7$. Therefore, the smallest number which can be divided from $3087$ to get the quotient as a perfect cube is $3 \times 3 = 9$.
What is the smallest number by which 4116 must be multiplied to obtain a perfect cube?∴ We must multiply 18 (2×3×3) to make 4116 a perfect cube.
What is the smallest number by which 106480 may be multiplied so that the product is a perfect cube?This is Expert Verified Answer
So the smallest number by which 106480 can be multiplied to become a perfect cube is 100.
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