Question

prove that
$5 - \frac{3}{7} \sqrt{3}$
is an irrational no. ​

Answer 1

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Let it be a rational number.

5 - 3/7 √3 = a/b

=> -3/7 √3 = a/b - 5

=> 3/7 √3 = (5b-a) /b

√3 = 7( 5b-a) /3b

It seems that √3 is rational.

So, our assumption get wrong because √3 is irrational number so 5-3/7√3 is irrational.

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