Answer:
![\begin{array}{ccccccc}&Natural&Whole &Integer&Rational&Irrational&Real\\-3(3)/(9)&&&& \checkmark&&\checkmark\\√(11) &&&&&\checkmark &\checkmark\\125&\checkmark&\checkmark&\checkmark&\checkmark&&\checkmark\\4\cdot \sqrt[3]{125} &\checkmark&\checkmark&\checkmark&\checkmark&&\checkmark\\7.\overline {17} &&&& \checkmark&&\checkmark\end{array}]()
Explanation:
The given numbers and their categories are;
1)
is not a natural number, because, natural numbers are whole number positive integers. It is not an integer, because it is a fraction.
It is a real number, because it has no imaginary part and it is a rational number because it can be expressed as a fraction
2) √11 is not a rational number, because it cannot be expressed as a fraction, and it is real number because it has no imaginary parts.
Therefore, is an irrational and real number
3) 125; The options selected are correct
4) 4·∛125 = 4 × 5 = 20; The options selected are correct
5) 7.
= 710/99; Therefore, 7.
is a rational number and it is also a real number as all natural, whole, integers, rational, and irrational numbers are real numbers
We get;
![\begin{array}{ccccccc}&Natural&Whole &Integer&Rational&Irrational&Real\\-3(3)/(9)&&&& \checkmark&&\checkmark\\√(11) &&&&&\checkmark &\checkmark\\125&\checkmark&\checkmark&\checkmark&\checkmark&&\checkmark\\4\cdot \sqrt[3]{125} &\checkmark&\checkmark&\checkmark&\checkmark&&\checkmark\\7.\overline {17} &&&& \checkmark&&\checkmark\end{array}]()