Simplify square root of 25-x^2+ square root of x+3

$\sqrt{25 - x^{2}} + \sqrt{x + 3}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} - x^{2}} + \sqrt{x + 3}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 5$ and $b = x$ .

$\sqrt{(5 + x) (5 - x)} + \sqrt{x + 3}$