Question 720688
{{{4sqrt(2) + 3sqrt(8)}}}
Like radical terms have the same kinds of roots with the same radicands. ("Radicand" is the name for the expression inside a radical.) So these are not like terms and cannot be added (yet).<br>
But the second square root's radicand has a perfect square factor so it will simplify:
{{{4sqrt(2) + 3sqrt(4*2)}}}
{{{4sqrt(2) + 3sqrt(4)*sqrt(2)}}}
{{{4sqrt(2) + 3*2*sqrt(2)}}}
{{{4sqrt(2) + 6sqrt(2)}}}
After simplifying, we find that we now have like terms. (Both are square roots and both radicands are 2's.) So we can add them. And <i>exactly</i> like 4x + 6x = 10x:
{{{4sqrt(2) + 6sqrt(2)}}}
adds up to
{{{10sqrt(2)}}}