#### Answer

$r=3$

#### Work Step by Step

$Given : $$\sqrt (r+5)=$$2\sqrt (r-1)$
Squaring both sides, we get : $r+5=4(r-1)$r+5
$Thus,$$r+5=4r-4$
$r+5+4=4r-4+4$
$r+9=4r$
$r+9-r=4r-r$
$9=3r$
$Thus,$$r=9\div3=3$
Then,check by substituting r = 3 in the original equation :
$L.H.S=$$\sqrt (3+5)=\sqrt 8=2\sqrt 2$
$R.H.S=$$2\sqrt (3-1)=2\sqrt 2$
Since L.H.S = R.H.S,r = 3 is a solution