How to know if a square root is rational or irrational?

The square root of an integer is rational if the integer is a square. Otherwise, the root is irrational.

Example: √4 = √(2²) = 2, is rational. √3 is irrational.

(It can be helpful to memorize the squares of small integers, up to about 20 or 25.)

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

i belive those are the ones that are under 90 degreese.