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√3+√5 prove it is a irrational …

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√3+√5 prove it is a irrational number.

Posted by Akshat Raghuwanshi 5 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Coco Li 5 years, 11 months ago

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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CBSE > Class 10 > Mathematics