Tag: properties of irrational numbers

Questions Related to properties of irrational numbers

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} $

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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.

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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. $\sqrt{11}$

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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

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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

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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

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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

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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

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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