Question 289695
{{{-4sqrt(112)-3sqrt(128)+3sqrt(63)-2sqrt(7)}}}
The primary part of simplifying expressions with square roots is to factor out perfect squares in each square root, if any:
{{{-4sqrt(16*7)-3sqrt(64*2)+3sqrt(9*7)-2sqrt(7)}}}
Then you use the property of radicals, {{{root(a, x*y) = root(a, x)*root(a, y)}}}, to separate the perfect square factors into their own square roots:
{{{-4sqrt(16)*sqrt(7)-3sqrt(64)*sqrt(2)+3sqrt(9)*sqrt(7)-2sqrt(7)}}}
Now we can replace the square roots of the perfect squares:
{{{-4*4*sqrt(7)-3*8*sqrt(2)+3*3*sqrt(7)-2sqrt(7)}}}
which simplifies to:
{{{-16sqrt(7)-24sqrt(2)+9sqrt(7)-2sqrt(7)}}}
The first, third and fourth terms are like terms which we can add and subtract. This gives us:
{{{-9sqrt(7)-24sqrt(2)}}}
This is the simplified expression.