How do you simplify (√2+√5) /( √2-√5)?

1 Answer
Mar 16, 2018

Answer:

The simplified expression is #-(7+2sqrt10)/3#.

Explanation:

#color(white)=(sqrt2+sqrt5)/(sqrt2-sqrt5)#

#=((sqrt2+sqrt5))/((sqrt2-sqrt5))color(red)(*((sqrt2+sqrt5))/((sqrt2+sqrt5)))#

#=((sqrt2+sqrt5)(sqrt2+sqrt5))/((sqrt2-sqrt5)(sqrt2+sqrt5))#

#=((sqrt2+sqrt5)(sqrt2+sqrt5))/(sqrt2^2+sqrt2sqrt5-sqrt2sqrt5-sqrt5^2)#

#=((sqrt2+sqrt5)(sqrt2+sqrt5))/(2color(red)cancelcolor(black)(+sqrt10-sqrt10)-5)#

#=((sqrt2+sqrt5)(sqrt2+sqrt5))/(2-5)#

#=((sqrt2+sqrt5)(sqrt2+sqrt5))/(-3)#

#=(sqrt2^2+sqrt2sqrt5+sqrt2sqrt5+sqrt5^2)/(-3)#

#=(2+sqrt10+sqrt10+5)/(-3)#

#=(2+2sqrt10+5)/(-3)#

#=(7+2sqrt10)/(-3)#

#=-(7+2sqrt10)/3#

This is the answer. You can verify using a calculator:

https://www.desmos.com/calculator