How do you evaluate 2 square root of 3 - 4 square root of 2 + 6 square root of 3 + 8 square root of 2?

1 Answer
Mar 15, 2016

Answer:

#8sqrt(3)+4sqrt(2)#

Explanation:

#1#. Recall that you can add and subtract radicals if they have the same value in the square root sign. You can think of the #color(teal)("radical")# as a #color(teal)("variable")#. Thus, start by grouping all like terms together.

#color(red)2color(teal)(sqrt(3))# #color(orange)(-4)color(teal)(sqrt(2))# #color(blue)(+6)color(teal)(sqrt(3))# #color(purple)(+8)color(teal)(sqrt(2))#

#=color(red)2color(teal)(sqrt(3))# #color(blue)(+6)color(teal)(sqrt(3))# #color(orange)(-4)color(teal)(sqrt(2))# #color(purple)(+8)color(teal)(sqrt(2))#

#2#. Add/subtract as appropriate.

#=(color(red)2# #color(blue)(+6))color(teal)(sqrt(3))+(color(orange)(-4)# #color(purple)(+8))color(teal)(sqrt(2))#

#3#. Simplify.

#=color(green)(|bar(ul(color(white)(a/a)8sqrt(3)+4sqrt(2)color(white)(a/a)|)))#