Question

The value of x=7+underroot40 . then find the value ofunderroot x+1/underroot x

Answer 1

$1/ \sqrt{x} = 1/(\sqrt5+\sqrt2) = (\sqrt5 - \sqrt2)/((\sqrt5 +\sqrt2) (\sqrt5- \sqrt2))$$\sqrt{x} = \sqrt5 + \sqrt2$
$(\sqrt5- \sqrt2)/ (5-2) = (\sqrt5- \sqrt2)/3$$\sqrt x + 1/\sqrt x = \sqrt5 + \sqrt2+ (\sqrt5 - \sqrt2)/3$
$(2/3) (2\sqrt5 + \sqrt2)$