For this problem, you are going to square both sides of the equation:

(sqrt(x+11))^2=(sqrt(x)+1)^2

Which gives us:

x+11 = x+2sqrt(x) +1

We will then subtract both x and 1 from both sides of the equation giving us:

x+11-x-1 = x+ 2sqrt(x)+1-x-1

Then combine like terms:

10 = 2 sqrt(x)

Divide both sides by 2:

5=sqrt(x)

And square both sides again:

25 = x

Then check the answer in the original equation to see if it is extraneous:

sqrt(25+11) = sqrt(25)+1

sqrt (36) = 5+1

6=6

It checks!

The solution of the equation `sqrt(x+11) = sqrt(x)+1` has to be determined.

Taking the square of both sides of the equation does not affect the equation.

`(sqrt (x+11))^2 = (sqrt x + 1)^2`

`(x + 11) = x + 1 + 2*sqrt x`

`2*sqrt x = 10`

`sqrt x = 5`

x = 25

The solution of the equation `sqrt(x+11) = sqrt(x)+1` is x = 25