Question 176969
Evaluate:
{{{(8sqrt(2))(sqrt(8)-3sqrt(2)+7sqrt(32))}}}
Ok, the key thing here is to get all of the radicands (the numbers inside of the square root symbols) to = 2, if possible. Well, since you know that 8 and 32 are multiples of 2 this is possible. So here we go, step-by-step!
{{{(8sqrt(2))(sqrt(4*2)-3sqrt(2)+7sqrt(16*2))}}}
Now, {{{sqrt(4) = 2}}} so you can move that outside of the radical but leave the 2 inside. And, {{{sqrt(16) = 4}}} so you can move that outside of the radical leaving the 2 inside:
{{{(8sqrt(2))(2sqrt(2)-3sqrt(2)+7*4sqrt(2))}}} Multiply the 7*4 = 28
{{{(8sqrt(2))(2sqrt(2)-3sqrt(2)+28sqrt(2))}}} In the second set of parentheses, collect all of the {{{sqrt(2)}}}'s together.
{{{(8sqrt(2))(27sqrt(2))}}} Finally, perform the indicated multiplication, do the numbers first (8*27 = 216) then the radicals ({{{sqrt(2)*sqrt(2) = 2}}} to get:
{{{highlight(216*2 = 432)}}}