Prove that root 6 is irrational number
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if we will multiply root 2 and root 3 we will get root 6 is an irrational no.
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Let us contradict the fact that √6 is rational no.
So , a/b =√6 ( where a and b are coprimes)
Sq. both side
(a/b)^2= (√6)^2
a^2/b^2 = 6
a^2 / b^2 -6 =0
a^2 - 6b^2/ b^2=0
hence a , 6b are integer and are rational no. so ,√6 is also a rational no.
But this contradict the fact that √6is rational no. instead √6 is irrational no.
So , a/b =√6 ( where a and b are coprimes)
Sq. both side
(a/b)^2= (√6)^2
a^2/b^2 = 6
a^2 / b^2 -6 =0
a^2 - 6b^2/ b^2=0
hence a , 6b are integer and are rational no. so ,√6 is also a rational no.
But this contradict the fact that √6is rational no. instead √6 is irrational no.
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