what is 5 square root of x + 1 = 21?

5√x + 1 = 21
5√x = 21 - 1
5√x = 20
√x = 20/5
√x = 4
x = 4^2
x = 16

5√x + 1 = 21
5√x = 20
√x = 4
x = 16

Isolate x.

(Raising to the power of 1/2 is the same as square-rooting.)

5*(x+1)^(1/2)=21
(x+1)^(1/2)=21/5
((x+1)^(1/2))^2=(21/5)^2
x+1=(21/5)^2
x=(21/5)^2-1

Or, if you want to simplify:

x=(21^2)/(5^2)-(5^2)/(5/2)
x=((21^2)-(5^2))/(5^2)
x=416/25

Or, if you cared to type it out more clearly and meant 5*x^(1/2)+1=21:

5*x^(1/2)+1=21
5*x^(1/2)=20
x^(1/2)=4
(x^(1/2))^2=4^2
x=16

...Which is a much nicer answer.