Answer:
[tex]8\sqrt{5}+3\sqrt{30}[/tex]
Step-by-step explanation:
When we have any quantity being multiplied to an expression, we can use the distributive property. The distributive property says that [tex]a(b+c)=ab+ac[/tex]. In other words, we can distribute the outer number inside the parentheses.
Using the distributive property, we can then simplify the given equation as follows:
[tex]\sqrt{5}(8+3\sqrt{6})=8\sqrt{5}+3\sqrt{6}\sqrt{5}[/tex]
Finally, you should recall that when multiplying square roots, you can simply bring all the numbers inside of one root. For instance, [tex]\sqrt{2}*\sqrt{3}=\sqrt{2*3}=\sqrt{6}[/tex] (note, this does not work for addition or subtraction, only multiplication or division). Therefore, we can simplify [tex]\sqrt{6}\sqrt{5}=\sqrt{6*5}=\sqrt{30}[/tex].
Finally, we can combine our answer into [tex]\sqrt{5}(8+3\sqrt{6})=8\sqrt{5}+3\sqrt{6}\sqrt{5}=8\sqrt{5}+3\sqrt{30}[/tex]
