Question

prove that 5-root3 is an irrational number

Answer 1

Heya!
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▪We shall prove it by the Method of Contradiction !!

♦So let us Assume that 5 - √3 is a Rational Number.


=> 5 - √3 = r

=> -√3 = r - 5


Now , from the Equation!!.

➡We know that √3 is an irrational number.

➡So , the RHS cannot be Rational or the Equation will become False !


⭐Hence Our Assumption is Wrong !!


✔Therefore, 5 -√3 is Irrational !!

Answer 2

heya friend ___ ✋✋

here's your answer ____⏩⏩

$let \: 5 - \sqrt{3} \: be \: a \: rational \: number \\ therefore \:$
$5 - \sqrt{3 } = \frac{p}{q} \\ = > - \sqrt{3} = \frac{p - 5q}{q}$
since,

$- \sqrt{3} \: is \: not \: equal \: to \: \frac{p - 5q}{q}$
therefore our assumption was wrong..

5 - √3 is an irrational number

✌hope it helps u ✌

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