Respuesta :
Answer:
Square of a rational number is a rational number.
Step-by-step explanation:
Let m be a rational number. Thus, m can be written in the form of fraction [tex]\frac{x}{y}[/tex], where x and y are integers and [tex]y \neq 0[/tex].
The square of m = [tex]m\times m = m^2[/tex]
[tex]m^2 = \frac{x}{y} \times\frac{x}{y} = \frac{x^2}{y^2}[/tex]
It is clearly seen, that [tex]m^2[/tex], can be easily written in the form of fraction and the denominator is not equal to zero.
Hence, [tex]m^2[/tex] is a rational number.
This can also be understood with the help of the fact that rational numbers are closed under multiplication that is product of a rational number is also a rational number.
