Question

prove that √3-√5 is irrational number

Answer 1

HOLA

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Let us assume √3 - √5 as rational

$\sqrt{3} - \: \sqrt{5} = \: \frac{a}{b} \\ \\ square \: on \: both \: sides \\ \\ ( \sqrt{3 \: } - \: \sqrt{5} ) {}^{2} = (\: \frac{a}{b} ) {}^{2} \\ \\ ( 3 - \: 5 \: ) \: = \: \frac{a {}^{2} }{b {}^{2} } \\ \\ \: \frac{a { }^{2 } - \: 5}{b {}^{2} - 3 }$
Hence , a and B are both factors

Hence our assumption was wrong ( √3 - √5 ) is irrational

Answer 2

√3 = √3 and √5 = √5