How would you simplify #sqrt 7 (3-sqrt 7)+8 sqrt7#?

1 Answer
Johnson Z.
Mar 15, 2016

#11sqrt(7)-7#

Explanation:

#1#. Distribute the #sqrt(7)# to each term in the brackets.

#color(red)(sqrt(7))(3-sqrt(7))+8sqrt(7)#

#=color(red)(sqrt(7))*3-sqrt(7color(red)(*7))+8sqrt(7)#

#=3sqrt(7)-7+8sqrt(7)#

#2#. Since radicals are like variables, you can think of #color(blue)(sqrt(7))# in #3color(blue)(sqrt(7))# as a #color(blue)("variable")#. Thus, add #8sqrt(7)# to #3sqrt(7)#.

#=3sqrt(7)+8sqrt(7)-7#

#=color(green)(|bar(ul(color(white)(a/a)11sqrt(7)-7color(white)(a/a)|)))#

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