Question

Read out each of the following numbers carefully and specify the natural numbers in it.
 \[87,54,0, - 13, - 4.7,\sqrt 7 ,217,\sqrt {15} , - 87,3\sqrt {7,} 4.807,0.002,\sqrt {16} {\text{ and 2 + }}\sqrt 3 \] .
A. \[0,87,54,\sqrt {16} \]
B. \[87,54,\sqrt {16} ,217\]
C. 0,-13,-4.7,217,54.87
D. \[\sqrt 7 ,\sqrt {15} ,3\sqrt 7 ,\sqrt {16} ,2 + \sqrt 3 \]

Answer 1

Hint: Firstly, carefully look at the given numbers.
Now, decide whether the number is a natural number, whole number, integer, rational or irrational number.
Thus, sort out the natural numbers from the above sorting and choose the correct option accordingly.

Complete step-by-step answer:
In the given question, it is asked to find out natural numbers form the given numbers.
We know that Natural numbers start from 1 and go up to infinite.
So, option (A) is wrong as there is a 0 in it and 0 is not counted as a natural number.
Option (B) has all natural numbers.
Although \[\sqrt {16} \] is not a natural number, we can simplify \[\sqrt {16} \] as 4, which is a natural number.
Thus, Option (B) is the correct answer.
For further checking,
In option (C), there are 0, negative and irrational numbers. So, option (C) is also wrong.
In option (D), there are mostly irrational numbers. So, option (D) is also wrong.

Note: Natural numbers is a set of numbers starting from 1 up to infinite. It is denoted by N. Thus, \[N = \left\{ {1,2,3,4,5,..} \right\}\]
Whole numbers are a set of numbers starting from 0 up to infinite. It is denoted by W. Thus, \[W = \left\{ {0,1,2,3,4,...} \right\}\]
Integers is a set of all whole numbers and negative of all-natural numbers. It is denoted by Z. Thus, \[\;Z = \left\{ {..., - 3, - 2, - 1,0,1,2,3,...} \right\}\]
Rational numbers are a set of all numbers that are in the form of $\dfrac{p}{q}$ . It is denoted by Q. Thus, Q = \[\left\{ {\dfrac{p}{q}|p \in Z,q \in Z - \left\{ 0 \right\}} \right\}\] .
Irrational number is a set of all numbers that cannot be rationalized. It is denoted by I. For example, $\sqrt 2 $ is an irrational number.
Real numbers is a set of all numbers. It is denoted by R. Thus, R includes all natural, whole, rational, irrational numbers and integers.
 $\therefore N \subset W \subset I \subset Q \subset I \subset R$ .