is √3+√5 an irrational number?
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Let root 3 + roof 5 be
rational
root 3 + root 5 = P/q
(root 3 + root 5) sq=(P/
q)sq
3 +5 + 2 root 15 = P sq/
q Sq
root I5 = (Psq / qsq -7)
1/2
RHS is rational as all are
integers
⇒ LHS is also rational
but root 15 is irrational
⇒ root3 + root 5 is
irrational
rational
root 3 + root 5 = P/q
(root 3 + root 5) sq=(P/
q)sq
3 +5 + 2 root 15 = P sq/
q Sq
root I5 = (Psq / qsq -7)
1/2
RHS is rational as all are
integers
⇒ LHS is also rational
but root 15 is irrational
⇒ root3 + root 5 is
irrational
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