Chapter 1.3, Problem 1LC

To determine

To find: the name of subsets of the real numbers to which the number belongs.

Answer to Problem 1LC

  $\sqrt{11}$ is an irrational number.

Explanation of Solution

Given:

  $\sqrt{11}$ .

Concept used:

Number system or real number $\left(R\right)$

consist of two types namely:

Rational numbers and irrational numbers.

Rational numbers: all terminating or recurring decimals.

irrational numbers: all non -terminating and non- recurring decimals.

Rational numbers $\left(Q\right)$ is divided by two types:

Integers and non-integers.

Integers are those numbers which are in the form composite number without the fraction and non-integers are numbers in fractions.

Integers are further divided into two types as:

Negative numbers and whole numbers and whole number is further divided into two type as natural number and zero.

From the above description it is clear that the rational and irrational numbers together form the set of real numbers.

Calculation:

Consider the number:

  $\sqrt{11}$ .

Write the subset of the real numbers for which the number contains.

Here, $\sqrt{11}=\mathrm{3.316624........}$ .

A number which can be expressed in the decimal form is expressible as non-terminating and non-repeating decimal is called as irrational number.

  $11$ is not perfect square and $\sqrt{11}$ is an irrational no.

Hence, $\sqrt{11}$ is an irrational number.