Let y² – 2y + 1 = x and $\sqrt{x}+y=5$. The value of $x+\sqrt{y}$ equals ________. (Give the answer up to three decimal places)

y² – 2y + 1 = x

$\sqrt{x}+y=5$

$\Rightarrow \sqrt{x}=5-y$

⇒ x = (5 - y)²

⇒ y² – 2y + 1 = (5 – y)²

⇒ y² – 2y + 1 = 25 + y² – 10y

⇒ 8y = 24 ⇒ y = 3

x = (5 - y)² = (5 - 3)² = 4

x + √y = 4 + √3 = 5.732