Question

simplify [1+n(n+1)(n+2)(n+3)]^(1/2)

Answer 1

[1+(n^2+n)(n+2)(n+3)]^(1/2)=
[1+(n^2+n)(n^2+3n+2n+6)]^(1/2)=
[1+(n^2+n)(n^2+5n+6)]^(1/2)

Answer 2

=[1+(n^4+5n^3+6n^2+n^3+5n^2+6n)]^(1/2)

Answer 3

=[1+(n^4+6n^3+11n^2+6n)]^(1/2), that's as far as you can simplify..

Answer 4

lets try this
\[1+n(n+1)(n+2)(n+3)=(n(n+3)+1)^2\]
and thefore your answer is
\[n(n+3)+1\]