Question

show that 5-√3 is rational​

Answer 1

Step-by-step explanation:

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Answer 2

$\large{ \bold{ \red{ \underline{ \underline{Question...}}}}}$

$\large{ \sf{show \: that \: 5 - \sqrt{3} is \: irrational.}}$

$\large{ \bold{ \green{ \underline{ \underline{Solution...}}}}}$

$\large{ \bold{ \red{ \underline{ \underline{Proof = > }}}}}$

$\large{ \sf{ \to \: let \: us \: assume \: on \: the \: contrary}} \\ \large{ \sf{that \: 5 - \sqrt{3} is \: rational. then \: there \: exist}} \\ \large{ \sf{ \: coprime \:positive \: integers \: a \: and \: b \: such \: that..}} \\ \\ \large{ \sf{ \green{ \to \: 5 - \sqrt{3} = \frac{a}{b} }}} \\ \\ \large{ \sf{ \to \: 5 - \frac{a}{b} = \sqrt{3} }} \\ \\ \large{ \sf{ \to \: \frac{5b - a}{b} = \sqrt{3} }} \\ \\ \large{ \sf{ \to \: \sqrt{3} is \: rational}} \\ \large{ \red{ \sf{(a \: and \: b \: are \: integers \: so...}}} \\ \large{ \sf{ \red{ \boxed{ \frac{5b - a}{b} is \: a \: rational \: number.)}}}} \\ \\ \large{ \sf{ \green{ \to \: this \: contradicts \: the \: fact \: that}}} \\ \large{ \sf{ \green{ \: \sqrt{3} is \: irrational. \: so \: our \: assumption}}} \\ \large{ \sf{ \green{ \: is \: incorrect. \: hence..5 - \sqrt{3} \: is \: irrational.. }}}$

$\large{ \bold{ \purple{hence \: proved...}}}$