Question

Find the smallest natural number by which 1200 should be multiplied so that the square root of the product is a rational number

Answer 1

Solution:-
√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.

Answer 2

factors of 1200 are 2×2×2×2×3×5×5
√1200=2×2×√3×5
so,
if u multiple 3 to 1200
then,
3×1200
=3600
so, 3600 is a perfect square