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Prove that 1upon root 2 is …

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Prove that 1upon root 2 is irrational

Posted by Sonu Bisht 6 years, 9 months ago

CBSE > Class 10 > Mathematics

1 answers

Ram Kushwah 6 years, 9 months ago

We assume that 1/{tex}\sqrt2{/tex} is a rational no

So {tex}\frac ab=\frac{1}{\sqrt2}{/tex}

( Where and b are co-primes)

b=a{tex}\sqrt 2{/tex}

b²=2a²--------(1)

b² is divisible by 2 ,so b is divisible by 2-----(2)

Let b=2c( c is any integer)

b²=4c²

2a²=4c²

a²=2c²

So a²is divisible by 2,So a is divisible by 2-----(3)

From (2) and (3)

a and b are divisible by 2

But this contradict the assumption that a and b are co-prime ,So no common factor in and b except 1

Hence our assumption that 1/ {tex}\sqrt2{/tex} is wrong ,

Hence 1/{tex}\sqrt2{/tex} is a non prime number

0Thank You

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