Question

prove that √3+√7 are irrational number ...... plz answer this question .......

Answer 1

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Answer 2

let it be rational
means it is of form x/y where x and y are co prime integers and y not equal to 0
$\sqrt{3} + \sqrt{7} = \frac{x}{y}$
Squaring both sides....
$3 + 7 + 2 \sqrt{21} = \frac{ {x}^{2} }{ {y}^{2} }$
$10 + 2 \sqrt{21} = \frac{ {x}^{2} }{ {y}^{2} }$
$\frac{ {x }^{2} - 10 {y}^{2} }{2 {y}^{2} } = \sqrt{21}$
but it contradict the fact that x and y are co prime integers as root21 is irrational and x^2-10y^2/2y^2 is rational

this means our supposition is wrong
thus root3+root7 is irrational

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