What is the smallest number by which 1372 must be multiplied so that the product becomes a perfect cube?
Find the required perfect cube so obtained.
Answers
Answered by
0
Answer:
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perfect cube
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Answered by
65
Answer:
Step 1: We will find the prime factors of 1372
by prime factorisation method
1372 = 2 × 2 × 7 × 7 × 7
Step 2: Find the least number
If we see, the prime factors of 1372, 7 is in
the group of 3 i.e. it makes a cube but 2 is
not in a group of 3 i.e. it is not making a
cube.
•2 is the smallest number by which 1372 must be multiplied so that the product becomes a perfect cube.
Let's check:
→1372 x The least number
⇒1372 × 2
⇒ 2744
→
Hence, proved.
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