Prove that 2 root 3 by 5 is irrational

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Prove that 2 root 3 /5 is an irrational number

Answered by admin @


Let 2root 3 / 5 be a rational no. in the form a/b where, a and b are integers.

Now,

2root3 / 5 = a / b

2root3 = 5a / b

root3 = 5a / 2b

Here. since a/b is a rational no., so 5a / 2b is also a rational no.

Hereby, root3 should also be a rational no.

 

But this contradicts tha fact that root3 is a rational no.

So, our assumption is wrong and hence 2root3 / 5 is an irrational no.


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