Question

How do I Simplify V5(8+3V6) ???

Answer 1

Answer:

$8\sqrt{5}+3\sqrt{30}$

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 $a(b+c)=ab+ac$.  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:

$\sqrt{5}(8+3\sqrt{6})=8\sqrt{5}+3\sqrt{6}\sqrt{5}$

Finally, you should recall that when multiplying square roots, you can simply bring all the numbers inside of one root.  For instance, $\sqrt{2}*\sqrt{3}=\sqrt{2*3}=\sqrt{6}$ (note, this does not work for addition or subtraction, only multiplication or division).  Therefore, we can simplify $\sqrt{6}\sqrt{5}=\sqrt{6*5}=\sqrt{30}$.  

Finally, we can combine our answer into $\sqrt{5}(8+3\sqrt{6})=8\sqrt{5}+3\sqrt{6}\sqrt{5}=8\sqrt{5}+3\sqrt{30}$