Tag: irrational numbers

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Multiple choice irrational numbers irrational numbers and their operations rational and irrational numbers real numbers (rational and irrational numbers) maths

State true or false:
The three rational numbers between $\displaystyle \sqrt{3}$ and $\displaystyle \sqrt{5}$ are 1.6, 1.8, 2.2

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We know that, $ \sqrt {3} = 1.732 $ and $ \sqrt {5} = 2.236 $





Hence three rational numbers between $ 1.732 $ and $ 2.236 $  can be $

1.8( = \frac {18}{10}) ; 2 $ and $ 2.2 (= \frac {22}{10}) $


Multiple choice irrational numbers irrational numbers and their operations rational and irrational numbers real numbers (rational and irrational numbers) maths

State the following statement is true or false:
$\dfrac{5}{12}$  lies between $\cfrac{1}{3}$ and $\cfrac{1}{2}$.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The average of the two numbers will be in between the two numbers.
$ \cfrac { \left( \dfrac { 1 }{ 3 }  \right) +\left( \dfrac { 1 }{ 2 }  \right)  }{ 2 } $

$= \cfrac { \left( \dfrac { 5 }{ 6 }  \right)  }{ 2 } $

$= \dfrac { 5 }{ 12 } $ is a rational number which lies between $\dfrac{1}{3}\ and\ \dfrac{1}{2}$. 




Multiple choice irrational numbers irrational numbers and their operations rational and irrational numbers real numbers (rational and irrational numbers) maths

State whether the given statement is true/false.
An irrational number between two numbers $\dfrac{1}{7}$ and $\dfrac{2}{7}$ is $0.1501500 15000...$ .

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Let us first find the decimal forms of the given numbers as follows: 
 
$\dfrac { 1 }{ 7 } =0.\overline { 142857 } ,\dfrac { 2 }{ 7 } =0.\overline { 285714 }$

We find a number which is non-terminating non-recurring lying between them.
So, we can find infinite many such numbers. For example, $0.150150015000...$ and $0.20200200020000....$

Hence, an irrational number between two numbers $\dfrac {1}{7}$ and $\dfrac {2}{7}$ is $0.150150015000...$
Multiple choice maths number systems existence of irrational numbers irrational numbers properties of irrational numbers

$A,B,C$ and $D$ are all different digits between $0$ and $9$. If $AB+DC=7B\ (AB,DC$ and $7B$ are two digit numbers), then the value of $C$ is

  1. $0$
  2. $1$
  3. $2$
  4. $3$
  5. $5$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

AB + DC = 7B. (10A + B) + (10D + C) = 70 + B. 10A + 10D + C = 70. A + D + C/10 = 7. Since A, D, C are digits, C must be 0 for the equation to hold with integer digits A and D. If C=0, A+D=7.

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

If $\sqrt{a}$ is an irrational number, what is a? 

  1. Rational

  2. Irrational
  3. $0$

  4. Real
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Consider the given irrational number$\sqrt{a}$ ,

Definition  of rational number- which number can be write in the form of $\dfrac{p}{q}$ but $q\ne 0$ is called rational number.

Hence, $a=\dfrac{a}{1}$

That why  $a$ is rational number

 

Hence, this is the answer.

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

Which of the following is irrational

  1. $\sqrt {\dfrac{4}{9}} $
  2. $\dfrac{4}{5}$
  3. $\sqrt 7 $
  4. $\sqrt {81} $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
A $=\sqrt{\dfrac{4}{9}}=\dfrac{2}{3}$         Rational

B $=\dfrac{4}{5}$                       Rational

C $=\sqrt7$                     Irrational

D $=\sqrt{81}=9$          Rational
Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

Which of the following rational number represents a terminating decimal expansion?

  1. $

    \dfrac { 77 } { 210 }

    $
  2. $

    \dfrac { 13 } { 125 }

    $
  3. $

    \dfrac { 2 } { 15 }

    $
  4. $

    \dfrac { 17 } { 18 }

    $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Any rational number its denominator is in the form of $2^m\times 5^n$, where $m,n$ are positive integer s are terminating decimals.

Solution is $B$ as $A$ is non terminating decimals.
$A =\dfrac{77}{210}= 0.366......$

$B =\dfrac{13}{125}= 0.104$

$C =\dfrac{2}{15}= 0.133.....$

$D =\dfrac{17}{18}=  0. 9444....$
Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

Read out each of the following numbers carefully and specify the natural numbers in it.
$87, 54, 0, -13, -4.7, \sqrt{7}, 2{1}{7}, \sqrt{15}, -{8}{7}, 3\sqrt{7}, 4.807, 0.002, \sqrt{16}$ and $2+\sqrt{3}.$

  1. $0,87,54,\sqrt{16}$
  2. $87, 54,$ $\sqrt{16}$, $217$
  3. $0, -13, -4,7, 217, 54, 87$
  4. $\sqrt{7}$, $\sqrt{15}$, $3 \sqrt{7}$, $\sqrt{16}$, $2 + \sqrt{3}$,
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Natural numbers from the given list are 87, 54,  $\sqrt { 16 } =4$ and 217