How do you simplify #(5+ sqrt 6) (5-sqrt 2)#?

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Answer 1 · 2016-09-05T04:05:34

#25+5(sqrt6-sqrt2)-2sqrt3#.

The Expression#=(5+sqrt6)(5-sqrt2)#

#=5(5-sqrt2)+(5-sqrt2)sqrt6#

#=25-5sqrt2+5sqrt6-sqrt2*sqrt6#

But, knowing that, #a^m*b^m=(ab)^m,# we find,

#sqrt2*sqrt6=2^(1/2)*6^(1/2)=(2*6)^(1/2)=12^(1/2)=(2^2*3)^(1/2)#

#=(2^2)^(1/2)*3^(1/2)=2^(1/2*2)*3^(1/2)=2^1*3^(1/2)=2sqrt3#

Finally, the simplified expression reads

#25+5(sqrt6-sqrt2)-2sqrt3#.

Enjoy Maths.!