$a) x^2-7=x^2-(\sqrt{7})^2=(x-\sqrt{7})(x+\sqrt{7})$
$b) x^2-22=x^2-(\sqrt{22})^2=(x-\sqrt{22})(x+\sqrt{22})$
$c) x^2+2\sqrt{7}x+7$
$=x^2+2.\sqrt{7}.x+(\sqrt{7})^2$
$=(x+\sqrt{7})^2$
$d) x^2-2\sqrt{23}x+23$
$=x^2-2.\sqrt{23}.x+(\sqrt{23})^2$
$=(x-\sqrt{23})^2$