Question

Help solving this radical!! FAN + MEDAL

Answer 1

\[\sqrt{1+4\sqrt{x}}=\sqrt{x}+1\]

Answer 2

square both sides

\[1 + 4\sqrt{x} = (\sqrt{x}+1)^2 = x + 2\sqrt{x}+1\]
combine terms
\[2 \sqrt{x} = x\]
square both sides again
\[4x = x^2\]
\[x^2 -4x = x(x-4) = 0\]
x = 0, x=4