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Prove that root3 is an irrational …

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Prove that root3 is an irrational number.

Posted by Akshay Kumar 1 year, 8 months ago

CBSE > Class 10 > Mathematics

2 answers

Harshita Saini 1 year, 8 months ago

Let √3 is rotational number :- √3 = p/q are co prime integers & q is not equal to 0 = 3 = p²/q² = P² = 3 × q²......(1) 3 is a factor of p² = 3 is a factor of p...(2) So p=3×m [m is any integer] (let) :- form (1) 9m²=3q² = q²=3m² :- 3 is a factor of q² = 3 is a factor of q.....(3) From (2) and (3) 3 is a common factor of both p&q It contradicts our supposition that p&q are co prime integers. Hence are supposition is wrong. :- √3 is irrational Hence proved

Itz__Kritika Koli 🖤 1 year, 8 months ago

Let √3 is rotational number :- √3 = p/q are co prime integers & q is not equal to 0 = 3 = p²/q² = P² = 3 × q²......(1) 3 is a factor of p² = 3 is a factor of p...(2) So p=3×m [m is any integer] (let) :- form (1) 9m²=3q² = q²=3m² :- 3 is a factor of q² = 3 is a factor of q.....(3) From (2) and (3) 3 is a common factor of both p&q It contradicts our supposition that p&q are co prime integers. Hence are supposition is wrong. :- √3 is irrational Hence proved

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