Tazmin Horton

2021-03-08

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

Firstly, remember that we can combine square roots. I.e. $\sqrt{8}\sqrt{18}$ is the same thing as $\sqrt{8×18}$.
Now let's factor that 8 and 18. The 8 can be factored as $8=2×2×2$ and the 18 as $18=2×3×3$
Thus $2\sqrt{8}\sqrt{18}=2\sqrt{8}×18=2\sqrt{2}×2×2×2×3×3$
Now remember that every pair of the same number can be pulled out from under the square root. For example, $\sqrt{2}×2=2$. With this in mind,$2\sqrt{2}×2×2×2×3×3=2×2×2×3=24$
And we're done!

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