The expression \sqrt{x} means the positive square root of x and is called a surd.
Surds such as \sqrt{2} can be evaluated on a calculator, for example \sqrt{2} = 1.414... \, \,, however this immediately introduces the issue of accuracy. Instead of evaluating, we use some algebraic properties of surds in order to simplify them, for example factors that are square numbers themselves.
Remember the all-important rules:

• \sqrt{ab} = \sqrt{a}\sqrt{b}
• \displaystyle \sqrt{\frac{a}{b} } =\frac{ \sqrt{a} }{\sqrt{b} }

Be aware also of these common mistakes when a and b are both positive:

• \sqrt{a + b} \ne \sqrt{a} + \sqrt{b}
• \sqrt{a - b} \ne \sqrt{a} - \sqrt{b}