How do you expand and simplify #(2+ \sqrt { 10} ) ( \sqrt { 5} + \sqrt { 20} )#?

1 Answer
Tony B
Nov 25, 2016

#6sqrt(5)" "+" "15sqrt(2)#

Explanation:

Multiply everything inside the right bracket by everything in the left.

#" "color(blue)((2+sqrt(10))color(brown)((sqrt(5)+sqrt(20))#

#color(brown)(color(blue)(2)(sqrt(5)+sqrt(20))color(blue)(" "+" "sqrt(10))(sqrt(5)+sqrt(20)))#

#2sqrt(5)+2sqrt(20)" "+" "sqrt(10)sqrt(5)+sqrt(10)sqrt(20)#

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But #sqrt(10)=sqrt(2)sqrt(5)" and "sqrt(20)=sqrt(4)sqrt(5)#
................................................................................................................

#2sqrt(5)+2sqrt(4)sqrt(5)" "+" "sqrt(2)sqrt(5)sqrt(5)+sqrt(2)sqrt(5)sqrt(4)sqrt(5)#

#" "2sqrt(5)+4sqrt(5)" "+" "5sqrt(2)+10sqrt(2)#

#" "6sqrt(5)" "+" "15sqrt(2)#

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