Question

show that 1/✓2 is a inrational number​

Answer 1

To show-

$\frac{1}{ \sqrt{2} } \: is \: \: an \: irrational \: \: number$

Solution -

$Let, \frac{1}{ \sqrt{2} } \: is \: \: rational$

Therefore we can find two integers x, y(y not equal to 0) such that,

$\frac{1}{ \sqrt{2} } = \frac{x}{y}$

$\sqrt{2} = \frac{y}{x}$

$\frac{y}{x} \: is \: rational \: \: as \: x\: and \: y \: are \: integers$

$\therefore \: \sqrt{2} \: is \: rational \: which \: \: contradicts \\ to \: \: the \: \: fact \: that \: \sqrt{2} \: is \: irrrational$

Hence our assumption is false

And,

$\frac{1}{ \sqrt{2} } \: is \: \: irrational$

Shown

Additional information -

• A number which can be written in the form of p/q, where p and q are integers and q not equal to 0 is called rational numbers.
• A number which cannot be written in the form of p/q, where p and q are integers and q not equal to 0 is called irrational numbers.