Advertisements
Advertisements
Question
The least number by which 72 be multiplied to make it a perfect cube is ______.
Advertisements
Solution
The least number by which 72 be multiplied to make it a perfect cube is 3.
Explanation:
Resolving 72 into prime factors, we get
72 = 2 × 2 × 2 × 3 × 3
Grouping the factors in triplets of equal factors, we get
72 = (2 × 2 × 2) × 3 × 3
We find that 2 occurs as a prime factor of 72 thrice, but 3 occurs as a prime factor only twice.
Thus, if we multiply 72 by 3, 3 will also occurs as a prime factor thrice and the product will be 2 × 2 × 2 × 3 × 3 × 3, which is a perfect cube.
Hence, the least number, which should be multiplied with 72 to get perfect cube, is 3.
APPEARS IN
RELATED QUESTIONS
Find the cube root of the following number by the prime factorisation method.
512
Find the cube root of the following number by the prime factorisation method.
10648
Find the cube root of the following numbers by the prime factorisation method.
27000
Find the cube root of the following number by the prime factorisation method.
15625
Find the cube root of the following number by the prime factorisation method.
110592
\[\sqrt[3]{\frac{27}{125}} = \frac{. . .}{5}\]
Three numbers are to one another 2 : 3 : 4. The sum of their cubes is 0.334125. Find the numbers.
Evaluate:
\[\sqrt[3]{96} \times \sqrt[3]{144}\]
Making use of the cube root table, find the cube root
8.6 .
Find the cube root of 13824 by prime factorisation method.
