Provide a beautiful proof of the following claim: the square of a rational number is a rational number.

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 , where x and y are integers and .

The square of m =

It is clearly seen, that , can be easily written in the form of fraction and the denominator is not equal to zero.

Hence, 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.

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b

the correct answer is b. negative exponential growth.

step-by-step explanation:

you can tell it's an exponential function because it decreases rapidly then levels out and never touches the x-axis.

it is negative because the y-axis decreases as the x-axis increases.

therefore it is a negative exponential growth graph.

hope i !