Question 450287
Multiplying square roots is very much like multiplying with variables. For example, if you have to multiply 2a and 10b, you would do (2*10)(a*b) = (20)(ab) = 20ab. In the same way, if you have {{{asqrt(b)*csqrt(d)}}}, you would turn that into {{{(a*c)(sqrt(b*d))}}}... basically, you multiply whatever is inside the square root sign together and whatever is outside the square root sign together.
Therefore, {{{4sqrt(10)*3sqrt(6) = (4*3)(sqrt(10*6)) = (12)(sqrt(60)) = 12sqrt(60)}}}
Next you have to simplify the square root by pulling whatever you can out.
First, factor the 60 in the square root:
{{{12sqrt(60) = 12sqrt(2*2*3*5)}}}
Next, for every pair of identical factors within the square root (such as 2 and 2), you can pull them out to equal one of the same factor outside of the square root; for example, in {{{3sqrt(2*3*3*7)}}}, you have two threes, so you can pull one out to equal {{{3*3sqrt(2*7)}}}, or {{{9sqrt(14)}}}
In this case, you have two twos, so you can pull out a two:
{{{12sqrt(2*2*3*5) = 12*2sqrt(3*5) = 24sqrt(15)}}}
Since three and five are different factors, you could not pull anything out.
==> Therefore, the final answer is {{{24sqrt(15)}}}
Hope that makes sense! =)
--Leaf