How do I multiply root numbers like 4(root)9 to 3(root)5 for an answer like x(root)y

The basic rule is

 $$\sqrt{ab}=\sqrt{a}\sqrt{b}.$$

So for example, (as a way of confirming the rule),

$$\sqrt{36}=\sqrt{9\times4}=\sqrt{9}\times\sqrt{4}=3\times2 = 6.$$

As an example of using the rule 'in reverse',

$$\sqrt{15}\times\sqrt{35}=\sqrt{15\times35}=\sqrt{525},$$

and it might, as in this case, be possible to take this a stage further.

$$\sqrt{15}\times\sqrt{35}=\sqrt{525}=\sqrt{25\times21}=\sqrt{25}\times\sqrt{21}=5\sqrt{21}.$$

Any odd numbers outside the square root signs are dealt with separately, so for example,

$$4\sqrt{3}\times 7\sqrt{2}=28\sqrt{6}.$$