Chapter 10 - Radical Expressions and Equations - 10-4 Solving Radical Equations - Practice and Problem-Solving Exercises - Page 623: 21

$v=7$

$Given,$ $\sqrt (7v-4)=\sqrt (5v+10) $ Squaring,we get: $7v-4=5v+10$ $7v-4+4=5v+10+4$ $7v-5v=14$ $2v=14$ $v=14\div2=7$ We need to check by putting the obtained value in the original equation : $L.H.S=\sqrt(7X7-4)=\sqrt (49-4)=\sqrt 45=\sqrt (5X7+10)=R.H.S$ Hence,$v=7$ is a valid solution