How do you add #2\sqrt { 50x } + \sqrt { 32x } - \sqrt { 2x }#?

1 Answer
Dwight
Apr 26, 2017

The total is #13sqrt(2x)#. Details follow...

Explanation:

Before you can combine terms, they must be shown to have the same value under the radical sign. We can factor each of the first two terms to leave #2x# inside the radical:

#2sqrt(50x) = 2sqrt(25*2x) = 2sqrt (25)*sqrt(2x) = 10sqrt(2x)#

Similarly,

#sqrt(32x) = sqrt(16*2x) = 4sqrt(2x)#

Putting it all together:

#10sqrt(2x) + 4sqrt(2x) - sqrt(2x) = 13sqrt(2x)#

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