Question

prove that
$\sqrt{5}$
is a rational number
​

Answer 1

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Answer 2

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Let √5 is a rational number.

Then √5 = a/b - ( where a and b, are co-prime and integers and b ≠ 0)

Squaring both sides

(√5 )² = ( a/b)²

5 b ² = a ² .., { i }

5 divides a ²

5 divides a

a = 5c - for some integers c.

a ² = 25 c ² ( squaring both sides)

5 b ² = 25 c ² .., { from i }

b ² = 5c ²

5 divides b²

5 divides b

5 divides both, a and b , means it contradicts our supposition that a and b are co-prime.

Hence, √5 is irrational number.

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