#### Answer

$a=16$

#### Work Step by Step

$Given,$ $\sqrt (3a+1)=7 $
Squaring,we get:
$3a+1=49$
$3a+1-1=49-1$
$3a=48$
$a=48\div3=16$
We need to check by putting the obtained value in the original equation :
$L.H.S=\sqrt (3X16+1)=\sqrt 49=7=R.H.S$
Hence,$a=16$ is a valid solution