Answer
$x=1$
Work Step by Step
$\sqrt {\sqrt {x+3} +\sqrt x} = \sqrt 3$
$(\sqrt {\sqrt {x+3} +\sqrt x})^2 = (\sqrt 3)^2$
$\sqrt {x+3} +\sqrt x = 3$
$\sqrt {x+3} +\sqrt x -\sqrt x= 3-\sqrt x$
$\sqrt {x+3} = 3-\sqrt x$
$(\sqrt {x+3})^2 = (3-\sqrt x)^2$
$x+3=3*3+3*(-\sqrt x)+(-\sqrt x)*3+(-\sqrt x)(-\sqrt x)$
$x+3=9-6\sqrt x +x$
$3=9-6\sqrt x$
$-6=-6\sqrt x$
$-6/-6 = -6\sqrt x/-6$
$1 = \sqrt x$
$1^2 = (\sqrt x)^2$
$1= x$
$\sqrt {\sqrt {x+3} +\sqrt x} = \sqrt 3$
$\sqrt {\sqrt {1+3} +\sqrt 1} = \sqrt 3$
$\sqrt {\sqrt {4} +1} = \sqrt 3$
$\sqrt {2 +1} = \sqrt 3$
$\sqrt 3 = \sqrt 3$ (true)
