Natural numbers is the set of counting numbers i.e. 1, 2, 3,…

So \(\displaystyle\sqrt{{80}}\) is not present in this set.

Whole numbers is the set of natural numbers along with 0 i.e. 0, 1, 2,…

So \(\displaystyle\sqrt{{80}}\) is not present in this set.

Integers are set of whole numbers along with negative numbers i.e. …,-2, -1, 0, 1, 2,…

So \(\displaystyle\sqrt{{80}}\) is not present in this set.

Rational numbers are set of numbers that can be expressed in the form \(\displaystyle\frac{{p}}{{q}}.\)

So \(\displaystyle\sqrt{{80}}\) is not present in this set.

Irrational numbers are set of numbers that cannot be expressed in the form \(\displaystyle\frac{{p}}{{q}}.\)

Hence \(\displaystyle\sqrt{{80}}\) is present in this set.

Real numbers are set of rational and irrational numbers together.

Hence \(\displaystyle\sqrt{{80}}\) is present in this set.

Answer: Irrational number and Real number.

So \(\displaystyle\sqrt{{80}}\) is not present in this set.

Whole numbers is the set of natural numbers along with 0 i.e. 0, 1, 2,…

So \(\displaystyle\sqrt{{80}}\) is not present in this set.

Integers are set of whole numbers along with negative numbers i.e. …,-2, -1, 0, 1, 2,…

So \(\displaystyle\sqrt{{80}}\) is not present in this set.

Rational numbers are set of numbers that can be expressed in the form \(\displaystyle\frac{{p}}{{q}}.\)

So \(\displaystyle\sqrt{{80}}\) is not present in this set.

Irrational numbers are set of numbers that cannot be expressed in the form \(\displaystyle\frac{{p}}{{q}}.\)

Hence \(\displaystyle\sqrt{{80}}\) is present in this set.

Real numbers are set of rational and irrational numbers together.

Hence \(\displaystyle\sqrt{{80}}\) is present in this set.

Answer: Irrational number and Real number.