If the constant on the right side is not a perfect square, the answers will be

rational

irrational

 Irrational

Step-by-step explanation:

Since it is not a perfect square thus the decimal expansion of that number is repeating or non-terminating. Hence it will an Irrational number. , where q≠0. The decimal which is non-terminating, non-repeating decimal expansion and thus it can't be written in the form of simple fraction is called irrational number.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is