How do you simplify and combine like radicals #sqrt32 - sqrt98 + sqrt50#?

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Answer 1 · 2015-04-09T06:38:46

First, we reduce each term to its Lowest/Standard Form

# sqrt32 = sqrt (16*2) = sqrt 16 * sqrt 2 = 4*sqrt 2#

# sqrt98 = sqrt (49*2) = sqrt 49 * sqrt 2 = 7*sqrt 2#

# sqrt50 = sqrt (25*2) = sqrt 25 * sqrt 2 = 5*sqrt 2#

#color(red)( sqrt32 - sqrt98 + sqrt50#

#= 4*sqrt 2 - 7*sqrt 2 + 5*sqrt 2 #

#= sqrt2*(4-7+5)#

#= sqrt2*(2)#

#= color(green)(2*sqrt2#