Find the smallest natural number by which 1200 should be multiplied so that the square root of the product is a rational number
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Find the smallest natural number by which 1200 should be multiplied so that the square root of the product is a rational number
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√1200
⇒ √100×12
⇒ √100×√12
⇒ 10×√4×3
⇒10×2√3
⇒ 20√3
Hence,
3 is the smallest natural number that needs to be multiplied with 1200, so as to make the product a rational number.
√1200=2×2×√3×5
so,
if u multiple 3 to 1200
then,
3×1200
=3600
so, 3600 is a perfect square