Question 424399
{{{2sqrt(2)+sqrt(32)}}}
Like radical terms are the same types of root with the same radicands. (The expression inside a radical is called a radicand.) Your terms are both the same kind of root, square root, but their radicands, 2 and 32, are not the same. So we cannot add these terms together.<br>
Although we cannot add these square roots we can simplify them if their radicands have any perfect square factors (other than 1). The first radicand, 2, is a prime number so it has no perfect square factors. But the second radicand, 32, does have a perfect square factor so we can simplify that square root.<br>
First we rewrite the radicand in factored form:
{{{2sqrt(2)+sqrt(16*2)}}}
Then we use a property of radicals, {{{root(a, p*q) = root(a, p)*root(a, q)}}}, to split the square root:
{{{2sqrt(2)+sqrt(16)*sqrt(2)}}}
The square root of the perfect square simplifies:
{{{2sqrt(2)+4sqrt(2)}}}
We have now simplified both square roots. And if you look again, you will see that we now have like terms! So now we can add them. And <i>exactly</i> like 2x + 4x = 6x:
{{{2sqrt(2)+4sqrt(2) = 6sqrt(2)}}}
So you expression simplifies down to {{{6sqrt(2)}}}