Tag: irrational numbers

Questions Related to irrational numbers

$0.\overline{35}$ is equal to

maths number systems existence of irrational numbers irrational numbers properties of irrational numbers

  1. $\displaystyle\frac{35}{66}$

  2. $\displaystyle\frac{35}{77}$

  3. $\displaystyle\frac{35}{99}$

  4. none of these

Show answer
Correct Option: C
Explanation:
$X=0.35353535$   -- i
Multiplying equation i with 100,

$100x=35.353535353$   --ii 
Subtracting equation i from ii 

$ 100x-x = 35.3535 - 0.3535 $
$99x=35$
$ x = \dfrac{35}{99}$

$3.\overline{25}$ is equal to

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

  1. $\displaystyle\frac{320}{99}$

  2. $\displaystyle\frac{321}{99}$

  3. $\displaystyle\frac{322}{99}$

  4. $\displaystyle\frac{323}{99}$

Show answer
Correct Option: C
Explanation:

Given that,$3.\overline{25}$.


Let,

$x=3.\overline{25}$

 $x=3.252525.....$


Multiply by 100 both sides,

  $ 100x=100\times 3.252525..... $

 $ 100x=325.2525..... $

 $ 100x=322+3.2525..... $

 $ 100x=322+x $

 $ 99x=322 $

 $ x=\dfrac{322}{99} $


Hence, this is the answer.

$0.\overline{05}$ is equal to

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

  1. $\displaystyle\frac{3}{99}$

  2. $\displaystyle\frac{4}{99}$

  3. $\displaystyle\frac{5}{99}$

  4. none of these

Show answer
Correct Option: C
Explanation:

Given that,$0.\overline{05}$

Let,

  $ x=0.\overline{05} $

 $ x=0.05050505..... $

Multiply by $100$ both sides,

 $ 100x=100\times 0.05050505..... $

 $ 100x=5.050505..... $

 $ 100x=5+0.050505..... $

 $ 100x=5+x $

 $ 99x=5 $

 $ x=\dfrac{5}{99} $


Hence, this is the answer.

Which statement is true?

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

  1. $ \displaystyle \frac{-8}{12} $= $ \displaystyle \frac{10}{-15} $

  2. $ \displaystyle \sqrt{3} $ is not a real number

  3. Additive identity of 5 is -5

  4. $ \displaystyle \frac{2}{5} $>$ \displaystyle \frac{4}{5} $

Show answer
Correct Option: A

Irrational number is defined as 

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

  1. a real number that cannot be made by dividing two integers.

  2. a real number that can be made by dividing two integer.

  3. a number that can be made derived after multiplying two integers.

  4. a real number that can be written as whole number.

Show answer
Correct Option: A
Explanation:
An irrational is any real number that cannot be expressed as a ratio of integers.

Therefore, $A$ is the correct answer.

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

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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.