What is the smallest natural number by which 54 must be divided to get a perfect cube?
Question 1: Find the cube roots of the following numbers by successive subtraction of numbers: 1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397, …(i) 64(ii) 512(iii) 1728Solution: Show
Question 2: Using the method of successive subtraction examine whether the following numbers are perfect cubes:(i) 130(ii) 345(iii) 792(iv) 1331Solution:
Question 3: Find the smallest number that must be subtracted from those of the numbers in question 2 which are not perfect cubes, to make them perfect cubes. What are the corresponding cube roots?Solution: In the previous question, there are three numbers that are not perfect cubes.
Question 4: Find the cube root of each of the following natural numbers:(i) 343 (ii) 2744 (iii) 4913 (iv) 1728 (v) 35937 (vi) 17576 (vii) 134217728 (viii) 48228544 (ix) 74088000 (x) 157464 (xi) 1157625 (xii) 33698267Solution:
Question 5: Find the smallest number which when multiplied with 3600 will make the product a perfect cube. Further, find the cube root of the product.Solution:
Question 6: Multiply 210125 by the smallest number so that the product is a perfect cube. Also, find out the cube root of the product.Solution:
Question 7: What is the smallest number by which 8192 must be divided so that quotient is a perfect cube? Also, find the cube root of the quotient so obtained.Solution:
Question 8: Three numbers are in the ratio 1:2:3. The sum of their cubes is 98784. Find the numbers.Solution:
Question 9: The volume of a cube is 9261000 m3. Find the side of the cube.Solution:
What number must be multiplies to 54 to make it a perfect cube?This is Expert Verified Answer
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 least number should 54000 be divided to get the result as a perfect cube?Hence the smallest number is 4.
How do you find the smallest number to be divided to get a perfect cube?Prime factorising 81, we get,. We know, a perfect cube has multiples of 3 as powers of prime factors.. Here, number of 3's is 4.. So we need to divide the factorization by 3 to make 81 a perfect cube.. Hence, the smallest number by which 81 must be divided to obtain a perfect cube is 3.. Is 1372 a perfect cube?∴ 1372 is not a perfect cube. Obviously, to make it a perfect cube we need one more 2 as its factor. which is a perfect cube. Thus, the required smallest number = 2.
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