3+√5 is a irrational number
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yes....... 3 + √5 is a irrational no.......
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Let us assume that √3+√5 is rational number.
A rational number can be written in the form of a/b where p,q are co-prime no.
√3+√5 = a/b
√3 = a/b-√5
by Squaring on both sides,
(√3)² = (a/b-√5)²
3 = a²/b²+√5²-2(a/b)(√5)
√5×2a/b = a²/b²+5-3
√5 = (a²+2b²)/b² × b/2p
√5 = (a²+2b²)/2ab
a,b are integers then (a²+2b²)/2pq is a rational number.
Then √5 is also a rational number.
But this contradicts the fact that √5 is an irrational number.
So,our assumption is false.
Therefore, √3+√5 is an irrational number.
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