# Real Numbers Examples

The pre-requisites to this lesson include the basic understanding of real numbers and its properties.

As we know a real number can be any natural , decimal , fraction , integer or whole number . Below are some such real number examples as well some problems related to them.

## Examples of real numbers

**1.** 0 /100 = 0 (rational , whole , integer)

**2.** 6 /2 = 3 (rational , natural, positive integer)

**3.** 3* 2^{-1 } (rational )

**4.** pi = 3.14159... (irrational)

**5.** 1/3 = 0.33333…. (rational)

**6.** (-1)^{-10} =1 (rational , natural, positive integer)

## Algebra Problems

The following problems will further clear your concepts regarding real numbers examples

**1. Evaluate 3x**^{2}** -2 x -1 where x =1**

**Solution**

Putting value of x in the given expression , we have

3x^{2} -2 x -1 = 3 (1)^{2 }- 2 (1) -1

= 3(1) – 2 -1

=3 -2-1

=0

So , answer is 0 which is a rational integer and whole number.

**2. Evaluate (x**^{3}**)**^{2}** where x = 1 **

**Solution**

Putting value of x , we have

(1^{3})^{2 }= ( 1 * 1 *1^{ })^{2}

= ( 1)^{2}

=1 * 1

=1

So , answer is 1 which is a rational natural number and positive integer.

**3. Evaluate (2**^{3}** * 2**^{-1}** * 2)**^{1/2}

**Solution**

Adding the exponents of all the numbers , we have

(2^{3} * 2^{-1} * 2)^{1/2} = ( 2^{3 + (-1) +1} )^{1/2}

= ( 2^{3 -1 +1} )^{1/2}

= (2^{1 })^{1/2}

= (2^{1 })^{1/2}

As a number raised to exponent 1/ 2 is equal to its square root , so we have

=

= 1.41421356...

So , the answer is 1.41421356... which is irrational number as it is non-terminating and non-recurring.

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