prove that√3 is an irrational number
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Step-by-step explanation:
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Answered by
1
Step-by-step explanation:
Proof : If possible let √3 is rational
then √3 = P/q where p & q are integers & q is not equal to 0
also, p & q are co - prines
now, √3 = p/q
( square both sides)
you get,
3 = p2/q2
3q2 = p2 ----(equation 1)
also 3 divides p2
=) 3 divides p
let p= 3r gor some integer
putting p = 3r (in equation 1)
we get,
3q2 = (3r)2
3q2 = 9r2
=} q2= 3r2
3 divides q2
3 divides q
this contradicts that P & q are co - primes
these contradiction arises due to our supposition that √ 3 is rational.
therefore, our supposition is wrong
Hence √ 3 is irrational.
....Hence proved
hope this helps you
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