Question

verify by calculating square root that √6 is not a rational number​

Answer 1

The following proof is a proof by contradiction.Let us assume that 6 is rational number. Then it can be represented as fraction of two integers. Let the lowest terms representation be: 6=ba where b=0Note that this representation is in lowest terms and hence, a and b have no common factorsa2=6b2From above a2 is even. If a2 is even, then a should also be even.⟹a=2c4c2=6b22c2=3b2From above 3b2 is even. If 3b2 is even, then b2 should also be even and again b is even.But a and b were in lowest form and both cannot be even. Hence, assumption was wrong and hence, 6 is an irrational number.

Answer 2

Answer

See here in this image

Square root of 6 by 2 by long division method is

=} 2.4494.......

this dot and dot means in last after 2.4494 means numbers are continuing and this no. has no end

and it is irrational

because it in continuing

And it is non terminating and non recurring