Question 817827
{{{sqrt(8)+3sqrt(8)-3}}}
The two square root terms are like terms. (Like radical terms are the same type of root and have the same radicands. ("Radicand" is the name for the expression inside a radical.) Our radicals are both square roots with radicands of 8 so we can add them together. <u>Exactly</u> like x + 3x = 4x, {{{sqrt(8)+3sqrt(8) = 4sqrt(8)}}}. After adding our expression is:
{{{4*sqrt(8)-3}}}<br>
All that is left is to simplify the square root. 8 has a perfect square factor, 4, so it will simplify:
{{{4*sqrt(4*2)-3}}}
{{{4*sqrt(4)*sqrt(2)-3}}}
{{{4*2*sqrt(2)-3}}}
which simplifies to:
{{{8*sqrt(2)-3}}}