Tag: existence of irrational numbers

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Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers
Which of the following is an irrational number?
  1. $\dfrac{11}{2}$
  2. $\sqrt{16}$
  3. $\sqrt{9}$
  4. $\sqrt{11}$
Reveal answer Fill a bubble to check yourself
D Correct answer
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.
Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

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

  1. an irrational number

  2. a composite number

  3. a rational number
  4. None of these as $m$ is not on a number line
Reveal answer Fill a bubble to check yourself
A Correct answer
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.
Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

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

  1. One

  2. Two

  3. Three

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

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

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?

  1. $1$ only
  2. $2$ only
  3. $3$ only
  4. $2$ and $3$
Reveal answer Fill a bubble to check yourself
C Correct answer
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