Question

How do you simplify `4sqrt(200)+8sqrt(49)-2sqrt2`?

Answer 1

I found: `38sqrt(2)+56`

Explanation:

I would change it by manipulating the arguments of the square roots:

`4sqrt(100*2)+8sqrt(7^2)-2sqrt(2)=`

`=4sqrt(100)*sqrt(2)+8sqrt(7^2)-2sqrt(2)=`

`=4*10sqrt(2)+8*7-2sqrt(2)=`

`=40sqrt(2)+56-2sqrt(2)=`

`=38sqrt(2)+56`

Answer 2

if `sqrt(49)=+7" "` then we have: `" "38sqrt(2)+56`

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Most people would go with the answer provided above.
if `sqrt(49)=-7" "` then we have: `" "38sqrt(2)-56`
You may also have a problem with`" "sqrt(2xx10^2)`

Explanation:

Try and identify common factors such that all the roots are the same. Where you can 'get rid' of the roots.

Write as:

`" "4sqrt(2xx10^2)+8sqrt(7^2)-2sqrt(2)`

`" "40sqrt(2)-2sqrt(2)+56`

`" "38sqrt(2)+56`
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However, `sqrt(49)=+-7`

So we could have:

`" "38sqrt(2)-56`