Question

q is a prime number then prove that root q is a irrational number

Answer 1

HOLA

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$let \: us \: assume \: \sqrt{q \: } \: as \: rational \\ \\ \sqrt{q} \: = \frac{a}{b} \\ \\ square \: on \: both \: sides \\ \\ (q) {}^{2} = ( \: \frac{a}{b}) { }^{2} \\ \\ \\ q {}^{2} = \: \frac{a {}^{2} }{b {}^{2} } \\ \\ qb {}^{2} = \: a {}^{2} \\ \\ q \: divides \: a { }^{2} \\ \\ q \: divdes \: a \\ \\ therefore \: \sqrt{q} \: is \: irrational$

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HOPE U UNDERSTAND ❤❤❤