Question

what is irrational number
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Answer 1

Irrational number, any real number that cannot be expressed as the quotient of two integers. ... Each irrational number can be expressed as an infinite decimal expansion with no regularly repeating digit or group of digits. Together with the rational numbers, they form the real numbers.

Answer 2

Step-by-step explanation:

$\star \bf \: Irrational \: numbers = numbers \: which \: cannot be \: expressed \: as\: the \\ \bf ratio \: of \: two \: whole \: numbers \: are \: known \: as \: irrational \: numbers$

$\bf \star \: examples \\ \bf π3 ,\: \: e \: , \sqrt{2} , \: \sqrt{3} \: , \sqrt{5}$

$\bf \star there \: are \: infinite \: irrationals \: between \: and \: two \: rational \: numbers.$

★ How to find irrational numbers ?

Take any two rational numbers a and b

Suppose x be any number between a and b

Then, we have a<x<b Eqn (i)

Now,

subtract √2 from both the sides of eqn (i)

$\bf⇒a− \sqrt{2} <x<b− \sqrt{2} ... Eqn (ii) \\ \bf⇒a<x+ \sqrt{2} <b$

Addition of irrational number with any number gives raise to an irrational number.

So, x+ √2 is an irrational number which exist between rational numbers a and b.