Tag: maths

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Questions Related to maths

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

A pair of irrational numbers whose product is a rational number is:

  1. $\sqrt{16}, \sqrt{4}$
  2. $\sqrt{5}, \sqrt{2}$
  3. $\sqrt{3}, \sqrt{27}$
  4. $\sqrt{36}, \sqrt{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In the given options,

for option $(A)$ $\sqrt { 16 } \& \sqrt { 4 }$ are not irrational numbers i.e. their real values are 4 & 2 respectively. It cannot be correct answer. 

Now multiplying other options, we get

$(B):\sqrt { 5 } \times \sqrt { 2 } =\sqrt { 10 } $

$(C)\sqrt { 27 } \times \sqrt { 3 } =\sqrt { 81 } =9$

$(D) \sqrt { 36 } \times \sqrt { 2 } =\sqrt { 72 } $

So, correct answer is option C.

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

A number is an irrational if and only if its decimal representation is :

  1. non terminating

  2. non terminating and repeating

  3. non terminating and non repeating

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

According to definition of irrational number, If written in decimal notation, an irrational number would have an infinite number of digits to the right of the decimal point, without repetition.

So, correct answer is option C.

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

Which of the following is not an irrational number?

  1. $5-\sqrt{3}$
  2. $\sqrt{5}+\sqrt{3}$
  3. $4+\sqrt{2}$
  4. $5+\sqrt{9}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We know that if add  or subtract any number from irrational number then the result will be irrational number.
$\sqrt { 5 } $ , $\sqrt { 3 }$ , $\sqrt { 2 } $  are irrational number but $\sqrt { 9 } $ =3 is a rational number so option D is correct answer 

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

$\pi$ is _______

  1. a rational number

  2. an integer

  3. an irrational number

  4. a whole number
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Sometimes we use $π = 22/7$ which is a popular approximation

$π = 3.14159265358...$

$22/7 = 3.142857142857...$

But $π$ and $22/7$ are close but not accurate.

Rational Numbers - $P/Q$ when $Q$ is not equal to $0$.

Let $x = 33.33333…. $——-(1)

$10x = 33.333333….. $——-(2)

Equation $(2) - (1)$

$9x = 30$

$x = 30/9$ which is in form of $P/Q$ and $x = 33.3333…$

The digit $‘3′$ is repeating itself and that’s why it can be written as $100/3.$

When it’s π, the value is $3.14159265358...$ The order of digits will not repeat itself in it but in $22/7 = 3.142857142857….$ you can see that $142857…$ is repeating itself that’s why $22/7$ is rational but $π$ is irrational.

So, option C is correct.
Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

Which of the following number is irrational ?

  1. $\sqrt{16}-4$
  2. $(3-\sqrt{3}) (3+\sqrt{3})$
  3. $\sqrt{5}+3$
  4. $-\sqrt{25}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In the given options $\sqrt { 16 }$ and $\sqrt { 25 } $ are irrational numbers. Their real values are 4 and 5 respectively. So, option A and C are incorrect.

Option B can solved and its real value becomes 6. So it is also a rational number.
In option C, $\sqrt { 5 }$ is a irrational number. So, option C is a irrational number. 
So, correct answer is option C. 

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

A number is an irrational if and only if its decimal representation is :

  1. non $-$ terminating
  2. non $-$ terminating and repeating
  3. non $-$ terminating and non $-$ repeating

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

Irrational numbers have decimal expansions that neither terminate nor repeating

So the correct answer is option C.

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. $\sqrt{23}$
  2. $\sqrt{225}$
  3. $0.3796$
  4. $7.478$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In the given options, 

$\sqrt { 225 }$ = 15. So, it is not a irrational number,
Option C and D are terminating decimals. So, they are also rational numbers.
$\sqrt{23}$ is a irrational number. 
So, option A is correct answer.  

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

$\pi$ is a(n) ________ while $\dfrac{22}{7}$ is rational.

  1. Integer

  2. Whole Number

  3. <p>Rational Number
    </p>

  4. <p>Irrational Number
    </p>
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The value $\dfrac{22}7$ is a rational number, as it can be expressed in the form $\dfrac pq$. 

We consider it as an approximate value of $\pi$ because $\pi$ is close to $\dfrac{22}7$. 
But actually its value is $3.14159....$, which is neither terminating nor repeating. 
Thus, $\pi $ is irrational, but $\dfrac{22}7$ is rational.