Question

Prove that 4-5√2 is irrational .​

Answer 1

Step-by-step explanation:

it is prove 4-5√2 is irrational number

Answer 2

$\huge \mathfrak \red{ÀÑẞWÈR}$

Step-by-step explanation:

$\red{Let \: us \: assume \: that \:  (4−5 \sqrt{2} ) \:  is \: rational .}$

Subtract given number from 4, considering 4 is rational number. as we know difference of two rational numbers is rational.

$4−(4−5 \sqrt{2} ) \: is \: rational$

$⇒5 \sqrt{2}   \: is \: rational$

$which \: is \: only \: possible \: if \:  5  \: is \: rational \: and  \sqrt{2}   \: is \: rational.$

As we know prouduct of two rational number s rational

$But \: the \: fact \: is  \sqrt{2} \:  is \: an \: irrational.$

Which is contradictory to our assumption.

$Hence,  \: 4−5 \sqrt{2}   \: is \: irrational . \: hence \: proved.$

$\pink{ \: i \: hope \: it \: helpfull \: for \: you}$