Firstly, remember that we can combine square roots. I.e. \(\displaystyle\sqrt{{{8}}}\sqrt{{{18}}}\) is the same thing as \(\displaystyle\sqrt{{{8}\times{18}}}\).

Now let's factor that 8 and 18. The 8 can be factored as \(\displaystyle{8}={2}\times{2}\times{2}\) and the 18 as \(\displaystyle{18}={2}\times{3}\times{3}\)

Thus \(\displaystyle{2}\sqrt{{{8}}}\sqrt{{{18}}}={2}\sqrt{{{8}}}\times{18}={2}\sqrt{{{2}}}\times{2}\times{2}\times{2}\times{3}\times{3}\)

Now remember that every pair of the same number can be pulled out from under the square root. For example, \(\displaystyle\sqrt{{{2}}}\times{2}={2}\). With this in mind, \(\displaystyle{2}\sqrt{{{2}}}\times{2}\times{2}\times{2}\times{3}\times{3}={2}\times{2}\times{2}\times{3}={24}\)

And we're done!

Now let's factor that 8 and 18. The 8 can be factored as \(\displaystyle{8}={2}\times{2}\times{2}\) and the 18 as \(\displaystyle{18}={2}\times{3}\times{3}\)

Thus \(\displaystyle{2}\sqrt{{{8}}}\sqrt{{{18}}}={2}\sqrt{{{8}}}\times{18}={2}\sqrt{{{2}}}\times{2}\times{2}\times{2}\times{3}\times{3}\)

Now remember that every pair of the same number can be pulled out from under the square root. For example, \(\displaystyle\sqrt{{{2}}}\times{2}={2}\). With this in mind, \(\displaystyle{2}\sqrt{{{2}}}\times{2}\times{2}\times{2}\times{3}\times{3}={2}\times{2}\times{2}\times{3}={24}\)

And we're done!