Question

Show that there is no rational number whose square is 3
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Answer 1

Explanation:

a rational number can be always expressed as fraction of two integers : x/y

if there would be a rational number with its square being 3, then we would have

x²/y² = 3

x² = 3y²

so, the squared rational number would have to be

3y²/y²

therefore, 3y² would have to be a squared number too.

and the basic number would then be sqrt(3)×y, which is not an integer. so, there can't be such a rational number.

Answer 2

`a^2 =3\\\\\implies a =\pm \sqrt 3\\\\\text{The value of a is irrational , so no such rational number exist.}`