Prove that root 6 is an irrational numbers

1.	Prove that root 6 is an irrational numbers
Answer» First assume that √6 is arational no. Then , √6= p by q form ,where p & q are integers ,q is not equals to zero and p&q are co-primes .Squaring both the sides 6= p sq. by q sq. = p sq.= 6q sq. -[1]i.e. p sq. is divisible by 6. So, p is also divisible by 6.Then , we can write p= 6rsquaring both the sides p sq.=12r sq.2 q sq= 4r sq. -[from equ. (1)]q sq. =4r sq. by 2 => q sq. =2r sq. -(2)i.e. q sq. Is divisible by 2So, q is also divisible by 6. Since, we can find p&q have a common factor between them (i.e. 2)In our contradicts & assumption √3 is not a rational number. It is an irrational no.

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