#### Answer

$v=-2$

#### Work Step by Step

$Given,$ $1=\sqrt (-2v-3) $
Squaring,we get:
$1=-2v-3$
$1+3=-2v-3+3$
$4=-2v$
$v=4\div-2=-2$
We need to check by putting the obtained value in the original equation :
$R.H.S=\sqrt (-2X-2-3)=\sqrt (4-3)=\sqrt 1=1=L.H.S$
Hence,$v=-2$ is a valid solution