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

Give an example of two irrational numbers, whose difference is an irrational number.

  1. $4\sqrt{3},2\sqrt{3}$
  2. $\sqrt{3},\sqrt{3}$
  3. $2\sqrt{3},2\sqrt{3}$
  4. $4\sqrt{3},4\sqrt{3}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let be the Number are $4\sqrt{3}  and  2\sqrt{3}$
Difference of Number  $4\sqrt{3} - 2\sqrt{3} = 2\sqrt{3}$
Which is a irrational number

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

Give an example of two irrational numbers, whose quotient is an irrational number.

  1. $\sqrt{15},\sqrt{5}$
  2. $\sqrt{45},\sqrt{5}$
  3. $\sqrt{20},\sqrt{5}$
  4. $\sqrt{80},\sqrt{5}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let be the Number are $\sqrt{15}  and  \sqrt{5}$
Quotient of Numbers  $\frac{\sqrt{15}}{\sqrt{5}} = \sqrt{\frac{15}{5}} = \sqrt{3} $
Which is a irrational number

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

Give an example of two irrational numbers, whose sum is an irrational number.

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

Let be the Number are $2\sqrt{5}  and  3\sqrt{5}$
Sum of Number  $2\sqrt{5} + 3\sqrt{5} = 5\sqrt{5}$
Which is a irrational number

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

Give an example of two irrational numbers, whose quotient is a rational number.

  1. $\sqrt{5},\sqrt{2}$
  2. $\sqrt{8},\sqrt{2}$
  3. $\sqrt{3},\sqrt{2}$
  4. $\sqrt{7},\sqrt{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let be the Number are $\sqrt{8}  and  \sqrt{2}$
Quotient of Numbers  $\frac{\sqrt{8}}{\sqrt{2}} = \sqrt{\frac{8}{2}} = \sqrt{4} = 2 $
Which is a rational number

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

Give an example of two irrational numbers, whose product is a rational number.

  1. $\sqrt{8},\sqrt{2}$
  2. $\sqrt{5},\sqrt{2}$
  3. $2+\sqrt{8},\sqrt{2}$
  4. $\sqrt{8},2+\sqrt{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let be the Number are $\sqrt{8}  and  \sqrt{2}$
Product of Numbers  $\sqrt{8}\times \sqrt{2} = \sqrt{16} = 4$
Which is a rational number

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

Give an example of two irrational numbers, whose product is an irrational number.

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

Let be the Number are $\sqrt{2}  and  \sqrt{3}$
Product of Numbers  $\sqrt{2}\times \sqrt{3} = \sqrt{6} $
Which is a irrational number

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

$\displaystyle log _{4}18$ is 

  1. an irrational number

  2. a rational number

  3. natural number

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

$  Log AB = log A + log B $
Also, $ log a^b = b log a $

So, $ log _{4} 18 = \frac { log 2 \times 3^2}{log 4}  = \frac { log 2 \times 3^2}{log 2^2}  = \frac { log 2}{2log 2} + \frac {2 log 3}{2 log 2}  = \frac {1}{2} +  \frac {log 3}{log 2}   $

As both $ log 2 $ and $ log 3 $ are irrational numbers, $ log _{x} 18 $ is an irrational number too. 

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

Number of integers lying between $1 $ to $102$  which are divisible by all $\displaystyle \sqrt{2},\sqrt{3},\sqrt{6}, $ is 

  1. $16$
  2. $17$
  3. $15$
  4. $0$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a number to be divisible by $\sqrt { 2 } $, it must be an irrational number. An integer is not an irrational,

so  there are no  numbers between  $ 1$ to  $102$ which are divisible by all  $\sqrt{2},\sqrt{3},\sqrt{6}$.

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

Simplify by combining similar terms :$\displaystyle 3\sqrt{147}-\frac{7}{3}\sqrt{\frac{1}{3}}+7\sqrt{\frac{1}{3}}$

  1. $\displaystyle \frac{189}{3\sqrt{3}}$
  2. $\displaystyle \frac{175}{3\sqrt{3}}$
  3. $\displaystyle \frac{208\sqrt{3}}{3}$
  4. $\displaystyle \frac{203}{3\sqrt{3}}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Simplify the expression: 3*sqrt(147) = 3*sqrt(49*3) = 21*sqrt(3). The other terms are -(7/3)(1/sqrt(3)) + 7(1/sqrt(3)) = (14/3)*(1/sqrt(3)) = 14/(3*sqrt(3)). Combining these requires a common denominator. The result is (21*3*sqrt(3) + 14)/(3*sqrt(3)) = (189+14)/(3*sqrt(3)) = 203/(3*sqrt(3)).