Question

3. Prove that
$\sqrt{5} \: is \: irrational.$


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Answer 1

Hey!!!

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Difficulty Level : Below Average

Chances of being asked in Board : 80%(regular question)

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By the method of Contradiction

Let √5 be a rational number

Then

$\sqrt{5} = \frac{p}{q} \: where \:$

p,q not equal to 0 and HCF (p,q) = 0

Thus

=> √5 = p/q

=> p = √5q

Square both sides

=> p² = 5q² ----------(1)

Thus p² is divisible by 5

=> p is also divisible by 5

Let p = 5m

Square both sides

=> p² = 25m²

=> 5q² = 25m² (from 1)

=> q² = 5m²

=> q² is divisible by 5

=> q is also divisible by 5

Here HCF(p,q) = 5 but it should be 1

Thus our assumption is wrong

Thus √5 is an Irrational number

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Answer 2

HEY mate here is your answer.

hope it helps you.