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Prove root 5 is rational number

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Prove root 5 is rational number

Posted by Md Arman 5 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

? Royal Thakur ? 5 years, 8 months ago

To prove that √5 is irrational number Let us assume that √5 is rational Then √5 = (a and b are co primes, with only 1 common factor and b≠0) ⇒ √5 = (cross multiply) ⇒ a = √5b ⇒ a² = 5b² -------> α ⇒ 5/a² (by theorem if p divides q then p can also divide q²) ⇒ 5/a ----> 1 ⇒ a = 5c (squaring on both sides) ⇒ a² = 25c² ----> β From equations α and β ⇒ 5b² = 25c² ⇒ b² = 5c² ⇒ 5/b² (again by theorem) ⇒ 5/b-------> 2 we know that a and b are co-primes having only 1 common factor but from 1 and 2 we can that it is wrong. This contradiction arises because we assumed that √5 is a rational number ∴ our assumption is wrong ∴ √5 is irrational number

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CBSE > Class 10 > Mathematics