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$\sqrt{2}$
%Enclose the entire radicand (also called the argument) in the braces.

$\sqrt{x^2 + y^2}$

$\sqrt{2 + \sqrt{2}}$

$\sqrt[4]{x}$
%Use square brackets in front of the braces to input a root other than 2.

About $3/4$ of the cake was eaten.

About $\frac{3}{4}$ of the cake was eaten.
%Use \frac{}{} to typset a fraction. Enclose the numerator in the first set of braces, and the denominator in the second set of braces.

$\frac{x}{x^2 + x + 1}$

$\frac{\sqrt{x-1}}{\sqrt{x + 1}}$
%For complex fractions, it helps to type all matching braces first, then go back and fill in the arguments.
%For example, step1: \frac{}{}, then step2: \frac{\sqrt{}}{}, then step3: \frac{\sqrt{}}{\sqrt{}}. Now fill in from the inside out.

$\frac{1}{1 + \frac{1}{x}}$

$\sqrt{\frac{x}{x^2 + x +1}}$

This expression, $\sqrt{\frac{x}{x^2 + x +1}}$, is quite complicated.

About $\displaystyle{\frac{3}{4}}$ of the cake was eaten.
%Use $\displaystyle{}$ to make expressions appear larger. This is particularly useful when typesetting fractions.

This expression, $\displaystyle{\sqrt{\frac{x}{x^2 + x +1}}}$, is quite complicated.

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