Math, asked by aanchalbang06, 10 months ago

show that 5-√3 is irrational

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Answered by tshivom9

Answer:

let us assum that 5-√3 is rational number so we can find two integers a , b. Where a and b are two co - primes number. So it arise contradiction due to our wrong assumption that 5 - √3 is rational number. Hence, 5 -√3 is irrational number.

Answered by XxMissPaglixX

${\huge{\mathtt{\pink{AnSwEr:-}}}}$

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$let \: (5 - \sqrt{3} ) \: be \: rational. \\ so \: 5 - \sqrt{3} = \frac{p}{q} \\ \sqrt{3} = 5 - \frac{p}{q} \\ \sqrt{3} = \frac{5q - p}{q} \\$

Here,

$\sqrt{3} \: is \: an \: irrational \: no. \: but \: \frac{5q - p}{q} \: is \: a \: rational \: no$

So,

$\sqrt{3} \: not \: = \frac{5q - p}{q} \\ which \: contradicts \: our \: supposition \: that \\ (5 - \sqrt{3} ) \: is \: rational$

$therefore \: (5 - \sqrt{3} ) \: is \: irrational.$

Hence Proved

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show that 5-√3 is irrational​

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So,

Hence Proved

show that 5-√3 is irrational