how can i sketch the graph Y=square root of x without the calculator?
The graph of $\displaystyle y = \sqrt{x} \: \: , \: x \geq 0$ is a common one and is usually known
However, if you draw the graph of $\displaystyle y = x^2 \: \: , \: x \geq 0$ and $\displaystyle y=x$ on the same axes then the graph you want will be the reflection of $\displaystyle y=x^2$ in the line $\displaystyle y=x$ (this is a property of all inverse functions)
edit: see attached graph - blue is y=x^2, green is y=x and orange is y = sqrt(x)