find the smallest natural number by which 1,200 shiuld be multiplied do that the square root of the product is a rational number
sanjanasingh98:
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I think it should be multiplied with 3.
1200×3=3600
It is a square root of 60
I am not sure about the answer: -)
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Answer:
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Step-by-step explanation:
For the square root to be rational, the number needs to be a square, and for this, each prime factor must occur with an even power.
The prime factorization of 1200 is
1200 = 2⁴ × 3¹ × 5²
The prime factors 2 and 5 already have even powers. The only one we need to fix is 3 and we get an even power here by multiplying by 3.
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