An irrational number is a number that cannot be expressed as a fraction and has a square root that is not a precise number.
Let's discuss each one:
Option A: √225 results into 15. The square root of 225 equals to 15, because 15 x 15 equals 225. And since 15 can be expressed as a whole integer, √225 is not an irrational number.
Option B: √49/9 equates to √(49/9) = √(7/3)^2 = 7/3. As 7/3 is a rational number, it can be expressed as a fraction and does not have an endless, non-repeating decimal. Hence, this is a rational number also.
Option C: √27 equals to about 5.196 which is not a perfect square and cannot be expressed as a fraction. Therefore, √27 is an irrational number.
Option D: √1 equals 1. Because 1 x 1 equals 1 and can be expressed as a fraction, √1 is not an irrational number.
From the above descriptions, we can conclude that in the provided options, B. √49/9 and C. √27 are irrational numbers.