Question

How to do long division for √2 by step for by examples?

Answer 1

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Answer 2

hey mate!!

here is u r answer!!!

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let as assume √2 be rational.then it will be of the form A/B,Where A,B are coprime integer and B does not equal to zero.

again ,let a and b have no common factor other than 1.

now,√2=A/B

on squaring both sides ,we get.

2=A square/b square

=2B square=A Square. eq(1)

=2 divides A Square
=2 divides A.

then,a can be written as 2m,in eq (1)we get.

2BSquare=2 m square

=2B square =4msquare =Bsquare =2msquare.

so ,2 divides B square=2 divide b

thus 2 is common factor of A andB.

but this contradict the fact that A and B have no common factor other than.this contradiction arises by assuming that√2is irrational.

hence,
√2 is irrational.

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I hope help u..