Question

is square root of every non square number always irrational?find the smallest natural number which divides 2205 to make its square root a rational number.

Answer 1

Thanks for asking the question.
Square root of a number which is not a perfect square is always irrational.
Irrational numbers are those which cannot be expressed as fractions.
Now,
in order to find a rational number in 2205, we will factorize it.
2205 is divided by 3, we get 735, which again divides on 3, giving 245. 245 is divided by 5, giving 49 which goes on 7 twice.
Here 5 is the smallest natural number that divides 2205 to make its square root a rational number.
Hope it helps.

Answer 2

Yes,  

The square root of every non perfect square number is always irrational. This is because the when we calculate the square root, the result does not stop before the decimal point. There are always non zero fractions. Also the fraction does not terminate.

  Express 2205 as a product of its factors.

   2205 = 5 * 441 
            = 5 * 21 * 21 
           =  5 * 3 * 3 * 7 * 7
  The only factor that is not appearing twice or appearing odd number of times is  5.

    So divide 2205 by 5 to get 441 which has a rational square root = 21.