How do you simplify #3sqrt.8 - 1sqrt.2#?

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Answer 1 · 2015-05-20T08:52:52

This expression cannot be simplified further without the use of a calculator.

Using a calculator:

#3sqrt.8-1sqrt.2# =

#(3xx0.894427191)-(1xx0.4472135955)=2.2360679775#

Answer 2 · 2015-05-20T10:31:39

You could actually get this to a simpler form.

#E = 3sqrt(.8) - sqrt(.2)#

#E = 3sqrt(8/10) - sqrt(2/10) = 3sqrt(8)/sqrt(10) - sqrt(2)/sqrt(10)#

#E = 1/sqrt(10) * (3sqrt(8) - sqrt(2)) | * sqrt(10)/sqrt(10)#

#E = sqrt(10)/underbrace(sqrt(10) * sqrt(10))_(color(blue)("=10")) * (3sqrt( 4 * 2) - sqrt(2))#

#E = sqrt(10)/10 * (3 * 2sqrt(2) - sqrt(2)) = sqrt(10)/stackrel(color(blue)(2))(cancel(10)) * cancel(5)sqrt(2)#

#E = (sqrt(10) * sqrt(2))/2 = sqrt(20)/2#

Using a calculator will indeed give you

#E = 2.236067...#