Given:

A number is given \(√ {\frac{9}{{11}}}\)

Concept:

Whole numbers are those numbers that started from 0 and go up to infinity.

Natural numbers are those numbers that started from 1 and go up to infinity.

Rational numbers are written in the form of p/q where q is not equal to zero and these are terminating decimals.

Irrational numbers are all the real numbers which are not rational numbers and it is the non-terminating and non-repeating decimals. 

Calculations:

We can solve it by option elimination method

\(√ {\frac{9}{{11}}}\) is neither a whole number nor a natural number because it is not expressed in the form of p/q

So, option (1) and option (2) is eliminated

\(√ {\frac{9}{{11}}}\) is not a rational number because denominator √11 is a non-terminating decimal and non-repeating decimal

So, option (3) is also eliminated

\(√ {\frac{9}{{11}}}\) is an irrational number because denominator √11 is a non-terminating decimal and non-repeating decimal

So, option (4) is the correct answer because √11 is a non-terminating and non-repeating decimal

∴ We can say that the \(√ {\frac{9}{{11}}}\) is an irrational number