First, we have to isoate the radical, by adding 5 both sides:

sqrt(x+1) - 5 + 5 = 3 + 5

sqrt(x+1) = 8

Now, we'll square both sides:

x+1 = 64

We'll isolate x by adding -1:

x = 64-1

x = 63

We'll verify the solution, substituting it into the equation:

sqrt(63+1) - 5 = 3

sqrt 64 - 5 = 3

8 - 5 = 3

3 = 3

So x=63 is the solution of the equation.

For this equation sqrt (x+1)-5=3, we need to add 5 from each side of the equation:

sqrt(x+1)-5+5= 3+5

sqrt(x+1)=8

Next, square both sides:

(x+1)=64

x+1-1= 64-1

x= 63

Verify equation by subsituting x=63 back into equation

sqrt(63+1)-5=3

sqrt64 -5=3

8-5=3

3=3

Thus, x=63 is the root of the equation.

To solve sqrt(x+1) -5 = 3.

Solution:

sqrt(x+1) -5 = 3. Add 5 to both sides. This makes known what is sqrt(x+1) :

sqrt(x+1) -5 +5 = 3+5. Simplyfy:

sqrt(x+1) = 8. Square both sides :

x+1 = 8^2 . Or

x+1 = 64. Subtract 1 from both sides:

x = 63,

Therefore for x =3, sqrt(63+1) -5 = 8-5 = 3 lolds good for sqrt(x+1)-5 = 3.