Tag: existence of irrational numbers

Questions Related to existence of irrational numbers

Which of the following is an irrational number?
maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

  1. $\dfrac{11}{2}$

  2. $\sqrt{16}$

  3. $\sqrt{9}$

  4. $\sqrt{11}$

Show answer
Correct Option: D
Explanation:
An irrational is any real number that cannot be expressed as a ratio of integers.
Option $A$ is a rational number.
Option $B$ and $C$ are $\sqrt{16}$ and $\sqrt{9}$, i.e. $4$ and $3$ respectively.
$D$ cannot be expressed as a ratio of integers.
$D$ is the correct answer.

The square root of any prime number is 

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

  1. rational

  2. irrational

  3. co-prime

  4. composite

Show answer
Correct Option: B
Explanation:

The square root of any prime number is irrational.
Example: $\sqrt{2}$ is a irrational number.

$\dfrac {7}{9}$ is a/an _______ number.

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

  1. rational

  2. composite

  3. irrational

  4. prime

Show answer
Correct Option: A
Explanation:

$\dfrac{7}{9}$ is of the form  $\dfrac {p}{q}$ form , hence it is rational no.


$\sqrt {23}$ is not a ...... number.

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

  1. irrational

  2. co-prime

  3. composite

  4. rational

Show answer
Correct Option: D
Explanation:

As per the theorem, the square root of any prime number is irrational. $\sqrt {23}$ is a prime number, so is not a rational number. It is irrational.
Therefore, $D$ is the correct answer.

$(3 + \sqrt {5})$ is .............. 

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

  1. whole number

  2. an integer

  3. rational

  4. irrational

Show answer
Correct Option: D
Explanation:

Sum or difference of a rational and irrational number is irrational. Therefore, $D$ is the correct answer.

$m$ is not a perfect square, then $\sqrt {m}$ is 

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

  1.  an irrational number

  2. a composite number

  3. a rational number

  4. None of these as $m$ is not on a number line

Show answer
Correct Option: A
Explanation:
$\sqrt {m}$ is irrational when it is not being a perfect square.
Example $\sqrt3$ which is an irrational number.

Therefore, $A$ is the correct answer.

$\pi = 3.14159265358979........$ is an

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

  1. rational number

  2. whole number

  3. irrational number

  4. all of the above

Show answer
Correct Option: C
Explanation:

$\pi = 3.14159265358979........$ is a non-terminating and non-repeating irrational number.

Hence, option $C$ is correct.

How many of the following four numbers are rational?
$\sqrt{3}+\sqrt{3}, \sqrt{3}-\sqrt{3}, \sqrt{3} \times \sqrt{3}, \sqrt{3} / \sqrt{3}$

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

  1. One

  2. Two

  3. Three

  4. Four

Show answer
Correct Option: C
Explanation:

$\sqrt { 3 } +\sqrt { 3 } =2\sqrt { 3 } \quad irrational\quad number\ \sqrt { 3 } -\sqrt { 3 } =0\quad rational\quad number\ \sqrt { 3 } \times \sqrt { 3 } =3\quad rational\quad number\ \frac { \sqrt { 3 }  }{ \sqrt { 3 }  } =1\quad rational\quad number$

Now it is clear that there are three rational number so correct answer will be option C

Which of the following are irrational numbers?

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

  1. $\log _{ 5 }{ 325 } $

  2. $\log _{ 10 }{ 5 } $

  3. $\log _{ 2 }{ 512 } $

  4. $\log _{ 2 }{ 3 } $

Show answer
Correct Option: A,B,D

Consider the following statements:
1. $\dfrac {1}{22}$ cannot be written as a terminating decimal.
2. $\dfrac {2}{15}$ can be written as a terminating decimal.
3. $\dfrac {1}{16}$ can be written as a terminating decimal.
Which of the statements given above is/are correct?

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

  1. $1$ only

  2. $2$ only

  3. $3$ only

  4. $2$ and $3$

Show answer
Correct Option: C
Explanation:

1/22 is an irrational number hence it is a non terminating number

2/15 is an irrational number hence it is a non terminating number
1/16 is an rational number hence it is a terminating number