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

2 Answers
May 16, 2018

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

(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)