Question

find the smallest natural number by which 1,200 should be multiplied so that the square root of the product is a rational number

Answer 1

√1200
⇒ √100×12
⇒ √100×√12
⇒ 10×√4×3
⇒10×2√3
⇒ 20√3
So, 3 is the smallest natural number that needs to be multiplied with 1200, so as to make the product a rational number.

Answer 2

Hey there,

Smallest natural no. by which 1200 should be multiplied = 3
            1200 × 3 = 3600
             √3600 = 60

Hope this helps!