Tag: rational and irrational numbers

Quizzes (6) Questions (185)

Questions Related to rational and irrational numbers

Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

Which of the following are irrational numbers?
(i) $\sqrt{2+\sqrt{3}}$
(ii) $\sqrt{4+\sqrt{25}}$
(iii) $\sqrt[3]{5+\sqrt{7}}$
(iv) $\sqrt{8-\sqrt[3]{8}}$.

  1. (ii), (iii) and (iv)

  2. (i), (ii) and (iv)

  3. (i), (ii) and (iii)

  4. (i), (iii) and (iv)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Option (i)

$\sqrt3$ is irrational, so (i) is irrational.

Option (ii)
$\sqrt{25} = 5$, so we get $\sqrt{4+5} = \sqrt9 = 3$ which is rational.

Option (iii)
$\sqrt7$ is irrational, so (iii) is irrational.

Option (iv)
$\sqrt[3]{8} = 2$, so we get $\sqrt{8-2} = \sqrt6$ which is irrational.

$\therefore$ (i),(iii) and (iv) are irrational.

Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

Which one of the following is an irrational number?

  1. $\pi$
  2. $\sqrt{9}$
  3. $\displaystyle\frac{1}{4}$
  4. $\displaystyle\frac{1}{5}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A number having non-terminating and non-recurring decimal expansion is  a Irrational Number


A number having non-terminating and recurring decimal expansion is  a Rational Number

now looking at the options

$\pi$  is an irrational number 

$\pi = 3.1415926535897932384626433832............$


the number has non-terminating decimal expansion and non-recurring.

$\sqrt9 = 3$  is a rational number

$\dfrac14 = 0.25$ is a rational number

$\dfrac15 = 0.2$ is a rational number

So option $A $ is correct

Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

Let $x$ be an irrational number then what can be said about ${x}^{2}$

  1. It is rational

  2. It can be irrational.

  3. It can be rational.
  4. Both $B$ and $C$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$x$ is any irrational number 
Let $x=\sqrt [ 4 ]{ 3 } $
$\Rightarrow { x }^{ 2 }=\sqrt { 3 } $
which is irrational so option $B$ is correct.
Now let $x=\sqrt 3$
$\Rightarrow {x}^{2}=3$
which is rational so option $C$ is correct.
So correct answer is $D$

Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

The product of a non-zero rational number with an irrational number is always :

  1. Irrational number

  2. Rational number

  3. Whole number

  4. Natural number
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

By definition, an irrational number in decimal form goes on forever without repeating (a non-repeating, non-terminating decimal). By definition, a rational number in decimal form either terminates or repeats. 

By multiplying a non repeating non terminating number to repeating or terminating/repeating number, the result will always be a non terminating non repeating number. 
So, option A is correct. 

Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

Which is not an Irrational number?

  1. $5-\sqrt{3}$
  2. $\sqrt{2}+\sqrt{5}$
  3. $4+\sqrt{2}$
  4. $6+\sqrt{9}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We know that sum of two irrational number or one rational and one irrational number will be irrational number. Option A, B , C stisfies this criteria but option D have two rational number i.e. $6 + \sqrt { 9 }$ = $6+ 3=9$

So correct answer is option D

Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

$\left ( 2+\sqrt{5} \right )\left ( 2+\sqrt{5} \right )$ expression is :

  1. A rational number

  2. A whole number

  3. An irrational number

  4. A natural number
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

${ (2+\sqrt { 5 } ) }^{ 2 }\ =4+5+4\sqrt { 5 } \ =9+4\sqrt { 5 } $

In the above equation $4\sqrt { 5 } $ is irrational number so $9+4\sqrt { 5 } $ will also be irrational number 
So correct answer is option C.

Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

A pair of irrational numbers whose product is a rational number is:

  1. $\sqrt{16}, \sqrt{4}$
  2. $\sqrt{5}, \sqrt{2}$
  3. $\sqrt{3}, \sqrt{27}$
  4. $\sqrt{36}, \sqrt{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In the given options,

for option $(A)$ $\sqrt { 16 } \& \sqrt { 4 }$ are not irrational numbers i.e. their real values are 4 & 2 respectively. It cannot be correct answer. 

Now multiplying other options, we get

$(B):\sqrt { 5 } \times \sqrt { 2 } =\sqrt { 10 } $

$(C)\sqrt { 27 } \times \sqrt { 3 } =\sqrt { 81 } =9$

$(D) \sqrt { 36 } \times \sqrt { 2 } =\sqrt { 72 } $

So, correct answer is option C.

Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

A number is an irrational if and only if its decimal representation is :

  1. non terminating

  2. non terminating and repeating

  3. non terminating and non repeating

  4. terminating
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to definition of irrational number, If written in decimal notation, an irrational number would have an infinite number of digits to the right of the decimal point, without repetition.

So, correct answer is option C.