Tag: properties 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 statement is true?

  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} $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Option A is correct because both fractions simplify to -2/3. Option B is false as sqrt(3) is a real number. Option C is false because the additive identity is 0, while -5 is the additive inverse of 5. Option D is false because 2/5 is less than 4/5.

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

Irrational number is defined as 

  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.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
An irrational is any real number that cannot be expressed as a ratio of integers.

Therefore, $A$ is the correct answer.

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