Question

I would appreciate the help...
Instructions: Multiply, and then simplify if possible. Assume all variables represent positive real numbers. Equation below

Answer 1

\[\left( 4\sqrt{7}+4 \right)(2\sqrt{7}+7)\]

Answer 2

\[\left( 4\sqrt{7}+4 \right)(2\sqrt{7}+7)\] step 1 is
\[4\sqrt7\times \sqrt7+4\sqrt7\times 7+4\times 2\sqrt7+4\times 7\] although you can do some in your head instead of writing it all out like this

Answer 3

for example, it should be clear that \(\sqrt7\times \sqrt7=7\) so the first term is really \(4\times 7=28\)

Answer 4

second term you can also do as you write is as \(4\sqrt7\times 7=4\times 7\sqrt7=28\sqrt7\)

Answer 5

similarly \(2\times 4\sqrt7=8\sqrt7\) and \(4\times 7=28\) so maybe a good first step it to write
\[28+28\sqrt7+8\sqrt7+28\] and then combine like terms

Answer 6

@satellite73 Thank you, I really needed the explanation, I'm studying for a final.Quick question though. In step 1 why is it
\[4\sqrt{7}\times7\] instead of \[4\sqrt{7}\times2\sqrt{7}\]

Answer 7

*forgot to add the square root to the 7

Answer 8

@Luigi0210 honestly the way it was explained is quite confusing, can you explain in another way without meshing all the numbers together

Answer 9

It's just like distributing, the only difference is that there's an extra number

Answer 10

So we have:
\[\LARGE {\left( 4\sqrt{7}+4 \right)(2\sqrt{7}+7)}\]
We would distribute the 4rad(7) and 2rad(7) first right?
So just think of it this:
\[\LARGE \left( 4\sqrt{7} \right)(2\sqrt{7})=(4*2)(\sqrt{7}*\sqrt{7})\]
Do know what that equals?

Answer 11

We're doing the first part, not the whole thing, yet.

Answer 12

So would it be 8*7

Answer 13

Right!
So now we do the next:
\[\LARGE 4\sqrt{7}*7\]
Since there's no square root, we just multiply the constants and leave it.
\[\LARGE (4*7)*(\sqrt{7})\]

Answer 14

\[28\sqrt{7}\]

Answer 15

Exactly, can you do the remaining two?

Answer 16

The same thing?

Answer 17

Yea, separate them if it helps.

Answer 18

Gah honestly I'm still a little confused...
so let me explain from the beginning and catch anything you see wrong please:)
\[4\sqrt{7}\times2\sqrt{7} \] equals \[8\times7=56\] then Multiply \[4\sqrt{7}\times7 \] which equals \[28\sqrt{7}\] Secondly multiply\[4\times2\sqrt{7}\] which then again equals to \[28\sqrt{7}\] lastly \[4\times7=28\] would it end up like this >>?
\[56+28\sqrt{7}+28\sqrt{7}+28\]
did I do something?I'm not confident about the 56

Answer 19

Ooops I see what I did wrong it's supposed to be \[8\sqrt{7}\]