Question

prove that
$\sqrt{3}$
is an irrational number

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Answer 1

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Answer 2

Question:-

prove that √3 is irrational .

Answer :-

proof :-

we are trying to prove that root 3 cannot be expressed as a fraction if we are trying to prove that something cannot be true it is often useful to assume that it is true and attempt to prove a contradiction .

so let us assume that ;

√3=a/b

where a/b is it fraction in its lowest term .

let us play around with this formula and see what we can come up with ;

√3=a/b

=> √3=a^2/b^2 [ squaring both the sides ]

=> 3b^2=a^2 [ multiplying b square ]

so A square is an even number => A is an odd number

we can therefore Express A as 3c where is the is also an integer .

=> 3b^2=a^2

=> 3b^2 =(3c)^2

=> 3b^2 = 9c^2

=> b^2= 3c^2

we can now see that b square is also even . and B is an odd number .

Assumption :-

but we can assume that a divided by b is a fraction in its lowest term which is clearly not since both A and B are even number so we have a contradiction and have to conclude that our original as a option that root 3 can be expressed as a fraction is false so we can say that root 3 is irrational