How do you rationalize the denominator and simplify #1/(sqrt2+sqrt5+sqrt3)#?

1 Answer

Answer:

Refer to explanation

Explanation:

We multiply and divide with #sqrt2+sqrt3-sqrt5# hence

#(sqrt2+sqrt3-sqrt5)/((sqrt2+sqrt3+sqrt5)*(sqrt2+sqrt3-sqrt5))= (sqrt2+sqrt3-sqrt5)/((sqrt2+sqrt3)^2-(sqrt5)^2)= (sqrt2+sqrt3-sqrt5)/(2+3+2sqrt2sqrt3-5)= (sqrt2+sqrt3-sqrt5)/(2sqrt2sqrt3)= (sqrt2+sqrt3-sqrt5)/(2sqrt6)= (sqrt6*(sqrt2+sqrt3-sqrt5))/(2sqrt6*sqrt6)= (sqrt12+sqrt18-sqrt30)/12#

Finally we have

#1/((sqrt2+sqrt3+sqrt5))=(sqrt12+sqrt18-sqrt30)/12= (2sqrt3+3sqrt2-sqrt30)/12#