The real number \( \sqrt{81/4} \) simplifies to \( 9/2 \), which is a rational and real number but not an integer or irrational.
To determine the classifications that apply to the real number \( \sqrt{\frac{81}{4}} \), we first simplify it. The square root of 81 is 9, and the square root of 4 is 2, so \( \sqrt{\frac{81}{4}} \) simplifies to \( \frac{9}{2} \). This number is a rational number because it can be expressed as a ratio of two integers.
It is also a real number, as all rational numbers are included in the set of real numbers. It is not an integer because it is not a whole number. Nor is it irrational, since irrational numbers cannot be expressed as a ratio of integers. Thus, the classifications that apply to \( \sqrt{\frac{81}{4}} \) are Rational and Real.