## Multiplying square roots to find triangle sides

Geometric formulae, word problems, theorems and proofs, etc.
AWOREK
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### Multiplying square roots to find triangle sides

If I am multiplying 2 square root of 2 by 2 square root of two, is the expression of that

( A ) 2 times square root of 4

( B ) 4 times square root of 4

I think it should be "B". But my teacher says it is "A". Why is it "A" ?

Why am I dropping one of the 2s ?

anonmeans
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### Re: Multiplying square roots to find triangle sides

If I am multiplying 2 square root of 2 by 2 square root of two,...
I'm taking this to mean $\left(2\, \sqrt{ 2\,}\right)\, \left(2\, \sqrt{ 2\,}\right)$.
...is the expression of that

( A ) 2 times square root of 4

( B ) 4 times square root of 4

I think it should be "B".
I get this:

\begin{align}\left(2\, \sqrt{ 2\,}\right)\, \left(2\, \sqrt{ 2\,}\right)\, &= (2)\, \left(\sqrt{2\,}\right)\, (2)\, \left(\sqrt{2\,}\right) \\ \\ &=\, (2)\, (2)\, \left(\sqrt{2\,}\right)\, \left(\sqrt{2\,}\right) \\ \\ &=\, (2\, \times\, 2)\, \left(\sqrt{2\,}\, \times\, \sqrt{2\,}\right) \\ \\ &=\, (4)\, \left(\sqrt{2\, \times\, 2\,}\right) \\ \\ &=\, 4\, \sqrt{4\,} \\ \\ &=\, 4\, \times\, 2 \\ \\ &=\, 8\end{align}

You can check by plugging the first thing into your calculator. Do you get 4 or do you get 8? I get 8, like what you said.