Tag: rational and irrational numbers

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Questions Related to rational and irrational numbers

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

Every surd is

  1. a natural number

  2. an irrational number

  3. a whole number

  4. a rational number
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
When a number cannot be simplified further to remove a square root then it is a surd.  
A surd is an irrational number.

For. eg: square root of 2 cannot be simplified. thus it is a surd.

By definition, a surd is an irrational root of a rational number. So we know that surds are always irrational and they are always roots.

For eg, $\sqrt2$ is a surd since 2 is rational and $\sqrt 2$ is irrational.

Similarly, the cube root of 9 is also a surd since 9 is rational and the cube root of 9 is irrational.

On the other hand, $\sqrtπ$ is not a surd even though $\sqrtπ$ is irrational because π is not rational.

Thus, to answer the question, every surd is an irrational number, though an irrational number may or may not be a surd.

The answer is Option B
Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

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

  1. $\displaystyle\frac{320}{99}$
  2. $\displaystyle\frac{321}{99}$
  3. $\displaystyle\frac{322}{99}$
  4. $\displaystyle\frac{323}{99}$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  1. $\displaystyle\frac{3}{99}$
  2. $\displaystyle\frac{4}{99}$
  3. $\displaystyle\frac{5}{99}$

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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.