Question 389875
{{{5sqrt(15)*(-2sqrt(3))}}}
This expression is all multiplication. So we can use the Commutative and Associative properties to rearrange the order and grouping to:
{{{(5*(-2))(sqrt(15)*sqrt(3))}}}
Multiplying the first part is simple. We use the property of radicals, {{{root(a, p)*root(a, q) = root(a, p*q)}}}, to multiply the square roots:
{{{-10sqrt(45)}}}
Last of all we simplify. We can simplify {{{sqrt(45)}}} because it has a perfect square factor, 9:
{{{-10sqrt(9*5)}}}
Now we can use the property of radicals (from right to left) to separate the factors into their won square roots:
{{{-10sqrt(9)*sqrt(5)}}}
Since {{{sqrt(9) = 3}}} this becomes:
{{{-10*3*sqrt(5)}}}
which simplifies to:
{{{-30sqrt(5)}}}