√()=
23×3×√3

A-CALCULATOR.COM

FAQs & How-to's

About This Calculator

  1. What is this calculator for?
  2. Can I embed this on my website?
  3. How can I do the math by hand?

What is this calculator for?

This calculator simplifies a surd so that the number below the radical 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/radical/embed.html" frameborder="0" allowtransparency="true"></iframe>

How can I do the math by hand?

To simplify radicals 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 its factors 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 radical 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.