#### Answer

The slant height is $3\sqrt 5$ cm.

#### Work Step by Step

Use the Pythagoras Theorem to solve for slant height (variable $x$):
$a^{2} + b^{2} = c^{2}$
When $c = x = $ hypotenuse of the right angled triangle
1. Substitute the $a$ and $b$ values to solve for $x$ into the equation
$(\sqrt 6)^{2} + (\sqrt 3)^{2} = (\sqrt x)^{2}$
$36 + 9 = x^{2}$
$45 = x^{2}$
$\sqrt 45 = x$
$3\sqrt 5 = x$
Therefore $x = 3\sqrt 5$ cm