siddh kijiye ki 3 + √5
ek aparimey sankhya hai
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Answered by
1
Answer:
3+√5 is an irrational number
Explanation:
therefore√5 is an irrational number but 3 is an rational number
when irrational number+rational number it give irrational number
hence 3+√5 is an irrational number
Answered by
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Let √3+√5 be a rational number.
A rational number can be written in the form of p/q where p,q are integers.
√3+√5 = p/q
√3 = p/q-√5
Squaring on both sides,
(√3)² = (p/q-√5)²
3 = p²/q²+√5²-2(p/q)(√5)
√5×2p/q = p²/q²+5-3
√5 = (p²+2q²)/q² × q/2p
√5 = (p²+2q²)/2pq
p,q are integers then (p²+2q²)/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 supposition is false.
Therefore, √3+√5 is an irrational number.
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