Question

Can you simplify this: sqrt((9t^4)+(18t^2)+9)

Answer 1

yes

Answer 2

Could you show me how?

Answer 3

factor out a 9 first and get
\[\sqrt{9(t^4+2t^2+1)}\]

Answer 4

then note that \(t^4+2t^2+1\) is itself a perfect square, namely
\[t^4+2t^2+1=(t^2+1)^2\]

Answer 5

this gives you
\[\sqrt{9(t^2+1)^2}\]

Answer 6

then take the square root and get \(3(t^2+1)\)