Tag: existence of irrational numbers

Use ______________ to represent an irrational number on number line.

$D$ is a real number with non terminating digits $a _1$ and $a _2$ after the decimal point. Let $D = 0, a _1 a _2 a _1 a _2 ........ $  with $a _1 & a _2$ both not zero which of the following when multiplied by $D$ will necessarily give an integer ?

The number $5\sqrt{34}$ lies between

Can $\sqrt { 3 } -3$ be represented on the number line. 

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

Which is the wrong step that shows $\displaystyle 5-\sqrt{3}$ is irrational?
(I) Contradiction : Assume that $\displaystyle 5-\sqrt{3}$ is rational
(II) Find coprime a & b $\displaystyle \left ( b\neq 0 \right )$ such that $\displaystyle 5-\sqrt{3}=\frac{a}{b},\therefore 5-\frac{a}{b}=\sqrt{3}$
Rearranging above equation $\displaystyle \sqrt{3}=5-\frac{a}{b}=\frac{5b-a}{b}$
(III) Since a & b are integers we get $\displaystyle 5-\frac{a}{b}$ is irrational and so $\displaystyle \sqrt{3}$ is irrational
(IV) But this contradicts the fact that $\displaystyle \sqrt{3}$ is irrational Hence $\displaystyle 5-\sqrt{3}$ is irrational

Which of the following irrational numbers lie between $4$ and $7$?

The ascending order of the surds $\sqrt[3]{2}, \sqrt[6]{3}, \sqrt[9]{4}$ is 

$A,B,C$ 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

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