How do you simplify #sqrt 5(sqrt 2+sqrt 10)#?

1 Answer
Pythagoras
Sep 25, 2015

#sqrt(10)(1+sqrt(5))# or #sqrt(2)(sqrt(5)+5)#

Explanation:

#sqrt(5)(sqrt(2)+sqrt(10))#
#=sqrt(5)*sqrt(2)+sqrt(5)*sqrt(10)#
#=sqrt(5*2)+sqrt(5)*sqrt(10)#
#=sqrt(10)+sqrt(5)*sqrt(10)#
#=sqrt(10)(1+sqrt(5))#

or

#sqrt(5)(sqrt(2)+sqrt(10))#
#=sqrt(5)*sqrt(2)+sqrt(5)*sqrt(10)#
#=sqrt(5)*sqrt(2)+sqrt(5*10)#
#=sqrt(5)*sqrt(2)+sqrt(50)#
#=sqrt(5)*sqrt(2)+sqrt(2*25)#
#=sqrt(5)*sqrt(2)+sqrt(2)*sqrt(25)#
#=sqrt(5)*sqrt(2)+5sqrt(2)#
#=sqrt(2)(sqrt(5)+5)#

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