Question

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

Answer 1

`1/44(5+7sqrt5)`

Explanation:

`sqrt5/(7-sqrt5)`

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

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

`1/44(5+7sqrt5)`

Answer 2

`(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)`