An irrational number is a number that cannot be expressed as a simple fraction or a ratio of two integers. Let's analyze the three options given:
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\( \sqrt{25} \): This is equal to 5, which is a rational number because it can be expressed as \( \frac{5}{1} \).
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\( \pi \): This is a well-known mathematical constant that represents the ratio of a circle's circumference to its diameter. It is an irrational number because it cannot be expressed as a fraction of two integers.
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\( 027 \): This seems to be a typo, but if you mean the number 27, it is equal to 27 and is also a rational number, as it can be represented as \( \frac{27}{1} \).
Thus, among the options given, \( \pi \) is the only irrational number.