√()=
23×3×√3

## FAQs & How-to's

#### What is this calculator for?

This calculator simplifies a surd so that the number below the square root sign doesn't have any perfect squares as factors.

#### Can I embed this on my website?

Sure. Embedding is allowed as long as you promise to follow our conditions. Here's the embed code:

 <iframe width="415" height="135" src="http://www.a-calculator.com/surd/embed.html" frameborder="0" allowtransparency="true"></iframe> 

#### How can I simplify radical expressions by hand?

To simplify surds you should know square numbers ($$2^2 = 4$$, $$3^2 = 9$$, $$4^2 = 16$$, etc). Using this knowledge you can break the number under the root sign into factors that are perfect squares like so: \begin{equation*} \sqrt{12} = \sqrt{4 \times 3} = \sqrt{2^2 \times 3} = \sqrt{2^2} \times \sqrt{3} = 2 \sqrt{3}. \end{equation*}

A surd is said to be in its simplest form when the number under the root sign has no square factors. For example $$\sqrt{72}$$ can be reduced to $$\sqrt{4 \times 18} = 2 \sqrt{18}$$. But $$18$$ still has the factor $$9$$, so we can simplify further: $$2 \sqrt{18} = 2 \sqrt{9 \times 2} = 2 \times 3 \sqrt{2} = 6\sqrt{2}$$. We stop at this stage seeing that $$2$$ has no square numbers as factors.