How do you simplify #sqrt5/(7-sqrt5)#?

2 Answers
May 16, 2018

Answer:

#1/44(5+7sqrt5)#

Explanation:

#sqrt5/(7-sqrt5)#

#=sqrt5/(7-sqrt5)xx(7+sqrt5)/(7+sqrt5)#

# = (7sqrt5+5)/(49-5)#

#1/44(5+7sqrt5)#

May 16, 2018

Answer:

#(7\sqrt5+5)/54#

Explanation:

#\sqrt(5)/(7-\sqrt(5))#
To remove the square root in the denominator, multiply by its conjugate:
#\sqrt(5)/(7-\sqrt(5))*(7+\sqrt(5))/(7+\sqrt(5))=(\sqrt(5)(7+\sqrt(5)))/((7-\sqrt(5))(7+\sqrt(5))#

Now simplify that.
#(7\sqrt5+5)/(49+\cancel(7\sqrt5-7\sqrt5)+5)#
#(7\sqrt5+5)/(49+5)=\color(tomato)((7\sqrt5+5)/54)#