√()=

2^{3}×3×√3

- What is this calculator for?
- Can I embed this on my website?
- How can I simplify radical expressions by hand?

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

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>
```

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.