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

2 Answers
Gió
Apr 22, 2016

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#

Tony B
Apr 22, 2016

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

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
However, #sqrt(49)=+-7#

So we could have:

#" "38sqrt(2)-56#

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