prove that √5+√3 js irrational
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let us assume
be a rational number
= √5 + √3= p/q, where as p,q€z,q notequal 0
=√5=p / q -√3,
by squaring on both the sides (√5) the whole square =(p/q - √3] the whole square
5= p square/ q square - 3.√3.p/q+3
3√3.p/q= p square /q square +3-3
be a rational number
= √5 + √3= p/q, where as p,q€z,q notequal 0
=√5=p / q -√3,
by squaring on both the sides (√5) the whole square =(p/q - √3] the whole square
5= p square/ q square - 3.√3.p/q+3
3√3.p/q= p square /q square +3-3
vigneshkumar1:
still the answer is not completed
= 3√3.p/q=p square /q square - 1 and (√3)3p/q=p square - q square /q square and √3 = ( p square - q square / q square) (q / 2p) and √3= p square - q square /2pq and √3 is a rational number hence p square -q square /2pq is a rational number . but √3 is not a rational number. this leads us to a contradiction the our assumption is wrong that √5+√3 is rational number therefore √5+√3 is an irrational number
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