Simplify: 2sqrt{8}sqrt{18}

Question
Simplify: $$\displaystyle{2}\sqrt{{{8}}}\sqrt{{{18}}}$$

2021-03-09
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!

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