Question

what is -2sqrt2p*2sqrt22

Answer 1

\[-2\sqrt{2p}*2\sqrt{22}\]

Answer 2

First multiply the two numbers not under the square roots. what do you get?

Answer 3

44p

Answer 4

only the -2 and 2 are NOT under the square root. what do you get?

Answer 5

-4

Answer 6

good. now look at the numbers under the square root. We have
\[ \sqrt{2}\cdot\sqrt{22}\cdot\sqrt{p} \]
If we split them.
We can combine the numbers:
\[ \sqrt{2 \cdot 22}\cdot \sqrt{p} \]

Answer 7

Now the important part. Notice that 22= 2*11, so we have under the square root
2*2*11 and the 2*2 is a square. Putting it all together (remember the -4 )
\[ −4\cdot 2\sqrt{11}\cdot\sqrt{p} \]
or
\[ −8\sqrt{11p} \]