Question 77807
{{{ graph( 300, 200, -6, 5, -10, 10, x, sqrt(x)) }}} graph of {{{y=x}}} and {{{y=sqrt(x) }}}

If you look the graph, you can see that {{{x<sqrt(x)}}} for the interval *[Tex \large (0,1)]. The reason is simply because the square root of a number reduces that number. The square root of a fraction, reduces the denominator if the numerator is 1. For instance, the square root of {{{1/4}}} is {{{1/2}}}. Since {{{1/2>1/4}}} it shows that {{{x<sqrt(x)}}} is true for values in (0,1).