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Prove that root 6 is an …

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Prove that root 6 is an irrational numbers

    • Posted by Ayush Kumar Gupta 7 years, 4 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Srijani Mitra 7 years, 4 months ago

    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= 6r squaring 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 2 So, 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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