# Prove that √3 +√5 is irrational.

2
by sanjays2402

2015-04-14T20:13:12+05:30

Suppose  is rational.
Multiplying both sides by  gives

Now

Which is a contradiction because is not rational.

The only resolution to this contradiction is that the starting assumption is wrong. That is,  is irrational.
Prove by taking a.
what a ? could you elaborate
2015-04-15T08:53:06+05:30
√3 +√5 let a is an rational number
√3 +√5 = asquaring on both sides
(√3 +√5 )² = a²3+5+2√3 √5  = a²
8+2√15 = a²
a²-8 = 2√15
= √15
if a is rational then  is also a rational
but √15 is a irrational
it is contradict to our assumption.
so √3 +√5 is not a rational