math assistance?

Question

i really need help with these last 2 problem of my math work, please help.

for this problem assume x is positive.
a.name three values of x for which the square root of x is less than x
b. name three valuesw of x for which the square root of x is greater than x
c. in general how can you tell whether square root of x is greater than x.

"Prove it!" evan said "if x^2=y^2, then x=y"
a. try several values of x and y to investigate evan's conjecture.
b.is evans conjecture true? if it is, explain why. if not give a counterexample

thank you fo helping me, its last minute and i will apreciate the help.

Answer 1

a. 2,3,4
b. 1/2, 1/4, 1/8
c. If x is greater then 1, the square root of x is less then x.
----
a. this should be fairly easy
b. this is false because of negatives - 1^2 is the same as -1^2, but 1 doesn't equal -1.

Answer 2

A.) sqrt x < x
in general, this is true of any positive number greater than 1
so: 4, 9, 64

B.) sqrt x > x
in general, this is true of any positive number less than 1
so: 0.25, 0.09, 0.16

C)
sqrt x < x ; true if x > 1
sqrt x > x ; true if 0 < x < 1

Answer 3

4.53234545656 and one half