how do I simpifly this, please show steps!(see pic below)

Question

anonymous · Answer

$$6\sqrt{2}-3\sqrt{2}$$

phi · Answer

if it were  6 x - 3 x  what would the answer be ?

phi · Answer

you have 6 of something and take away 3 of the same thing.  what do you have left ?

anonymous · Answer

3 if you take 3 from each side? @phi

phi · Answer

there is only 1 "side"    (you only have sides if you have an equation)

this is just   6 of something , take away 3 of that something

phi · Answer

if it were   6 cows, take away 3 cows,  how many cows ?

this is almost the same thing,  except instead of cows you have square roots of 2

radar · Answer

Let's do this the hard way, First factor the expression:$$3\sqrt{2}(2-1) = 3\sqrt{2}(1)= 3\sqrt{2}$$

radar · Answer

I'm sure that cleared that up even to the most casual observer, ........lol

anonymous · Answer

if you take away 3 from six you got three, will you please do it step by step on the equation drawing thing

phi · Answer

yes,  you have  
$$ 6 \sqrt{2} - 3 \sqrt{2} = 3 \sqrt{2} $$

that says you have 6 sqrt(2) and take away 3  sqrt(2), leaving 3 sqrt(2)

phi · Answer

the main idea is sqrt(2) is a number.  Treat it like any other number.  For example,

if the problem was

six 2's  take away three 2's  you are left with three 2's

it is the same for sqrt(2)

anonymous · Answer

okay, I think I got that last part?

phi · Answer

another way to think of the problem is

$$ 6 \sqrt{2} = \sqrt{2} +\sqrt{2} +\sqrt{2} +\sqrt{2} +\sqrt{2} +\sqrt{2} $$
and 
$$ 3 \sqrt{2} =  \sqrt{2} +\sqrt{2} +\sqrt{2}  $$
and
$$  6 \sqrt{2} - 3 \sqrt{2} =  \sqrt{2} +\sqrt{2} +\sqrt{2} +\sqrt{2} +\sqrt{2} +\sqrt{2} -  \sqrt{2} -  \sqrt{2} -  \sqrt{2} $$

phi · Answer

another way to think of it is use factoring like radar:

$$ 6 \sqrt{2} - 3\sqrt{2}= \sqrt{2}(6-3) $$
by "factoring out sqrt(2)"
simplify 6-3 to get 3 and the answer
$$ \sqrt{2} \cdot 3 $$
which is normally written with the 3 in front (but order does not matter when multiplying... it just looks nicer with the 3 in front)
$$ 3 \sqrt{2} $$

phi · Answer

do any of those make sense ?

phi · Answer

personally, I like to think it is the same as thinking of sqrt(2) as a cow, and we subtract  cows.

anonymous · Answer

thank you these last ones helped me a lot!

anonymous · Answer

$$3\sqrt{2}$$ @phi would this be the answer?

radar · Answer

That does agree with my first post.