Chapter 10 - Radical Expressions and Equations - 10-4 Solving Radical Equations - Practice and Problem-Solving Exercises - Page 623: 23

$n=4$

$Given,$ $\sqrt (n+5)=\sqrt (5n-11)$ Squaring,we get: $n+5=5n-11$ $n+5+11=5n-11+11$ $n+16-n=5n-n$ $4n=16$ $s=16\div4=4$ We need to check by putting the obtained value in the original equation : $L.H.S=\sqrt(4+5) =\sqrt 9=3=\sqrt (5X4-11)=\sqrt (20-11)=R.H.S$ Hence,$n=4$ is a valid solution