prove that root 6 is irrational
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Assume that √6 is rational
√6= where p and q are coprime
P = √6q
Squaring both sides
P2 = (√6q)2
P2 = 6q2
p2 = 36q2
p and q are factors of both p and p2 -----------------(1)
take p = 6r
squaring on both sides
p2 = 6r2
but p2 = 36q2
36q2 = 36r2 ----------------( 2)
from 1 and 2
this is a contradiction to our assumption
therefore , root 6 is irrational
Now on dividing from 5 on both sides we get,
=
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