Question 350866
{{{(-5sqrt(6))(2sqrt(3))}}}
Since this expression is all multiplication and since multiplication is commutative and associative, we change change the grouping and/or order <i>in any way we choose</i>. So I am going to rearrage the factors so that the coefficients are together and grouped and the square roots are together and grouped:
{{{((-5)(2))(sqrt(6)*sqrt(3))}}}
The first part is easy to multiply. To multiply the square roots we need to know a basic property of radicals: {{{root(a, p)*root(a, q) = root(a, p*q)}}}. We can use this to multiply square roots. Now we have:
{{{(-10)(sqrt(6*3))}}}
which simplifies to
{{{-10sqrt(18)}}}
We are almost done. Just like you should reduce/simplify answers that are fractions, you also should simplify square roots. To simplify a square root you look for perfect square factors in the radicand (the expression inside the square root). Since 18 has a perfect square factor, 18 = 9*2, we can simplify, using the property we used eariler:
{{{-10sqrt(9*2)}}}
{{{-10sqrt(9)*sqrt(2)}}}
Since {{{sqrt(9) = 3}}}:
{{{-10*3*sqrt(2)}}}
which simplifies to:
{{{-30sqrt(2)}}}