Question

So i'm practicing for my ACT compass test and i've come across this questions
Saying that 4 < √x < 9 is equivalent to saying what about x ?
A. 0 < x < 5
B. 0 < x < 65
C. 2 < x < 3
D. 4 < x < 9
E. 16 < x < 81
Now after researching everyone is giving me answer E and i understand that... BUT..
The answer sheet says its B... WHY! I don't understand @.@

Answer 1

Take the square of each term
4 < √x < 9
4^2 = 16
9^2=81
(√x ) = ?

Answer 2

Maybe its a misprint?

Answer 3

Last one should be
(√x )^2 = ?

Answer 4

Answer sheet is wrong.

Answer 5

Bingo.

Answer 6

You think?.. UG.. stupid test -_-

Answer 7

Draw the graph and see....Clearly, when sqrt(x) is between 3 and 4, then we get 9 < x < 16. You could also just square each part of the inequality to get the same solution. Note that we discard our negative x-values since the co-domain of sqrt(x) is restricted and hence we only look at the principal root and ignore the negative roots.