find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube part first 243
Answers
Answer:
the smallest natural number by which 243 should be multiplied to make it a perfect cube is 3.
Step-by-step explanation:
In the prime factorization of a perfect cube every prime factor occurs 3 times.
To determine whether a number is a perfect cube or not proceed as follows:
1.Find the prime factors of the given number.
2. Make Group of 3 equal prime factors.
3. If a group contains only one or two equal prime factors then a given number is not a perfect cube otherwise it is a perfect cube.
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Solution:
(i) Prime factors of 243 = (3 × 3 × 3) × 3 × 3
Here, two 3s are left which are not in a triplet. To make 243 a cube, one more 3 is required.so, we multiply 243 by 3 to make it a perfect cube.
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 it a perfect cube is 3.