Question

prove that (root3 + root5)whole square is an irrational number

Answer 1

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Solution ―
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Let √3 + √5 be rational

=> √3 + √5 - a , where a is rational

=> √3 = a - √5 ....... ( 1 )

on squaring both sides of equation ( 1 ) , we get

3 = ( a - √5 ) ^2 = a^2 +5 + 2√5a

=> √5 = a^2 + 2 / 2a

This is impossible because right hand side is rational , whereas the left hand side is irrational .

This is a contradiction .

Hence , √3 + √5 is irrational .

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